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Volumn 249, Issue , 1998, Pages 1-172

Square root problem for divergence operators and related topics

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EID: 0000740667     PISSN: 03031179     EISSN: None     Source Type: Book Series    
DOI: None     Document Type: Article
Times cited : (214)

References (82)
  • 2
    • 0011833753 scopus 로고
    • La conjecture de Kato pour les opérateurs différentiels elliptiques à coefficients périodiques
    • Série 1
    • G. ALEXOPOULOS - La conjecture de Kato pour les opérateurs différentiels elliptiques à coefficients périodiques, C. R. Acad. Sci. Paris 312, Série 1 (1991), p. 263-266.
    • (1991) C. R. Acad. Sci. Paris , vol.312 , pp. 263-266
    • Alexopoulos, G.1
  • 3
    • 77957128250 scopus 로고    scopus 로고
    • Analysis of second order elliptic operators without boundary conditions with VMO or Hölderian coefficients
    • Multiscale wavelets methods for partial differential equations (Dahmen, Kurdila, Oswald, ed.), Acad. Press
    • J. ANGELETTI, S. MAZET and P. TCHAMITCHIAN - Analysis of second order elliptic operators without boundary conditions with VMO or Hölderian coefficients, Multiscale wavelets methods for partial differential equations (Dahmen, Kurdila, Oswald, ed.), Wavelets and its Applications, vol. 6, Acad. Press, 1997.
    • (1997) Wavelets and Its Applications , vol.6
    • Angeletti, J.1    Mazet, S.2    Tchamitchian, P.3
  • 4
    • 84968488966 scopus 로고
    • Bounds for fundamental solutions of a parabolic equation
    • D. ARONSON - Bounds for fundamental solutions of a parabolic equation, Bull. Amer. Math. Soc. 73 (1967), p. 890-896.
    • (1967) Bull. Amer. Math. Soc. , vol.73 , pp. 890-896
    • Aronson, D.1
  • 5
    • 0001092529 scopus 로고    scopus 로고
    • Regularity theorems and heat kernels for elliptic operators
    • P. AUSCHER - Regularity theorems and heat kernels for elliptic operators, J. London. Math. Soc. 54 (1996), p. 284-296.
    • (1996) J. London. Math. Soc. , vol.54 , pp. 284-296
    • Auscher, P.1
  • 7
    • 0001450470 scopus 로고    scopus 로고
    • Absence de principe du maximum pour certaines équations paraboliques complexes
    • P. AUSCHER, T. COULHON and P. TCHAMITCHIAN - Absence de principe du maximum pour certaines équations paraboliques complexes, Coll. Math. 171 (1996), p. 87-95.
    • (1996) Coll. Math. , vol.171 , pp. 87-95
    • Auscher, P.1    Coulhon, T.2    Tchamitchian, P.3
  • 8
    • 0001732817 scopus 로고    scopus 로고
    • Holomorphic functional calculi of operators, quadratic estimates and interpolation
    • P. AUSCHER, A. MCINTOSH and A. NAHMOD - Holomorphic functional calculi of operators, quadratic estimates and interpolation, Indiana Univ. Math. J. 46 (1997), p. 375-403.
    • (1997) Indiana Univ. Math. J. , vol.46 , pp. 375-403
    • Auscher, P.1    Mcintosh, A.2    Nahmod, A.3
  • 9
    • 0041047691 scopus 로고    scopus 로고
    • The square root problem of Kato in one dimension, and first order systems
    • _ The square root problem of Kato in one dimension, and first order systems, Indiana Univ. Math. J. 46 (1997), p. 659-695.
    • (1997) Indiana Univ. Math. J. , vol.46 , pp. 659-695
  • 11
    • 0002697426 scopus 로고    scopus 로고
    • Heat kernel of complex elliptic operators and applications
    • _ Heat kernel of complex elliptic operators and applications, J. Funct. Anal. 152 (1998), p. 22-73.
    • (1998) J. Funct. Anal. , vol.152 , pp. 22-73
  • 12
    • 0040793791 scopus 로고
    • Ondelettes et conjecture de Kato
    • Série 1
    • P. AUSCHER and P. TCHAMITCHIAN - Ondelettes et conjecture de Kato, C. R. Acad. Sci. Paris 313, Série 1 (1991), p. 63-66.
    • (1991) C. R. Acad. Sci. Paris , vol.313 , pp. 63-66
    • Auscher, P.1    Tchamitchian, P.2
  • 13
    • 0001227990 scopus 로고
    • Conjecture de Kato sur les ouverts de ℝ
    • _ Conjecture de Kato sur les ouverts de ℝ, Rev. Mat. Iberoamericana 8 (1992), p. 149-199.
    • (1992) Rev. Mat. Iberoamericana , vol.8 , pp. 149-199
  • 14
    • 0011495883 scopus 로고
    • Calcul fonctionnel précisé pour des opérateurs elliptiques complexes en dimension un (et applications à certaines équations elliptiques complexes en dimension deux)
    • _ Calcul fonctionnel précisé pour des opérateurs elliptiques complexes en dimension un (et applications à certaines équations elliptiques complexes en dimension deux), Ann. Inst. Fourier 45 (1995), p. 721-778.
    • (1995) Ann. Inst. Fourier , vol.45 , pp. 721-778
  • 15
    • 0030305236 scopus 로고    scopus 로고
    • Square roots of divergence operators, square functions and singular integrals
    • _ Square roots of divergence operators, square functions and singular integrals, Math. Research Letters 3 (1996), p. 429-437.
    • (1996) Math. Research Letters , vol.3 , pp. 429-437
  • 17
    • 33748040659 scopus 로고
    • Commutators of singular integral operators
    • A. CALDERÓN - Commutators of singular integral operators, Proc. Nat. Acad. Sci. USA (1974), p. 1324-1327.
    • (1974) Proc. Nat. Acad. Sci. USA , pp. 1324-1327
    • Calderón, A.1
  • 18
    • 0002793072 scopus 로고
    • Polynomial growth estimates for multilinear singular integral operators
    • M. CHRIST and J.-L. JOURNÉ - Polynomial growth estimates for multilinear singular integral operators, Acta Math. 159 (1987), p. 51-80.
    • (1987) Acta Math. , vol.159 , pp. 51-80
    • Christ, M.1    Journé, J.-L.2
  • 19
    • 0001450011 scopus 로고
    • Domaine de la racine carrée de certains opérateurs différentiels accrétifs
    • R. COIFMAN, D. DENG and Y. MEYER - Domaine de la racine carrée de certains opérateurs différentiels accrétifs, Ann. Inst. Fourier 33 (1983), p. 123-134.
    • (1983) Ann. Inst. Fourier , vol.33 , pp. 123-134
    • Coifman, R.1    Deng, D.2    Meyer, Y.3
  • 21
    • 0003300591 scopus 로고
    • Non-linear harmonic analysis and PDE
    • Beijing Lectures in Harmonic Analysis (E. M. Stein, ed.), Princeton Univ. Press
    • R. COIFMAN and Y. MEYER - Non-linear harmonic analysis and PDE, Beijing Lectures in Harmonic Analysis (E. M. Stein, ed.), Annals of Math. Studies, vol. 112, Princeton Univ. Press, 1986.
    • (1986) Annals of Math. Studies , vol.112
    • Coifman, R.1    Meyer, Y.2
  • 23
    • 33748077662 scopus 로고
    • Real-analytic operator-valued functions defined
    • (C. Sadosky, ed.), Marcel Dekker
    • R. COIFMAN and S. SEMMES - Real-analytic operator-valued functions defined in BMO, Volume in honor of M. Cottar (C. Sadosky, ed.), Marcel Dekker, 1991.
    • (1991) BMO, Volume in Honor of M. Cottar
    • Coifman, R.1    Semmes, S.2
  • 25
    • 0003279962 scopus 로고
    • Wavelets and singular integrals on curves and surfaces
    • Springer-Verlag
    • G. DAVID - Wavelets and singular integrals on curves and surfaces, Lecture Notes in Math, vol. 1565, Springer-Verlag, 1991.
    • (1991) Lecture Notes in Math , vol.1565
    • David, G.1
  • 26
    • 0001720260 scopus 로고
    • A boundedness criterion for generalized Calderón-Zygmund operators
    • G. DAVID and J.-L. JOURNÉ - A boundedness criterion for generalized Calderón-Zygmund operators, Ann. Math. 120 (1984), p. 371-398.
    • (1984) Ann. Math. , vol.120 , pp. 371-398
    • David, G.1    Journé, J.-L.2
  • 27
    • 0002350898 scopus 로고
    • Opérateurs de Calderón-Zygmund, fonctions para-accrétives et interpolation
    • G. DAVID, J.-L. JOURNÉ and S. SEMMES - Opérateurs de Calderón-Zygmund, fonctions para-accrétives et interpolation, Rev. Mat. Iberoamericana 1 (1985), p. 1-56.
    • (1985) Rev. Mat. Iberoamericana , vol.1 , pp. 1-56
    • David, G.1    Journé, J.-L.2    Semmes, S.3
  • 29
    • 0001431987 scopus 로고
    • Uniformly elliptic operators with measurable coefficients
    • _ Uniformly elliptic operators with measurable coefficients, J. Funct. Anal. 132 (1995), p. 141-169.
    • (1995) J. Funct. Anal. , vol.132 , pp. 141-169
  • 30
    • 0002721868 scopus 로고    scopus 로고
    • p regularity of selfadjoint elliptic operators
    • p regularity of selfadjoint elliptic operators, J. Diff. Eqns. 135 (1997), p. 83-102.
    • (1997) J. Diff. Eqns. , vol.135 , pp. 83-102
  • 31
    • 0002412307 scopus 로고
    • Sulla differenziabilità e l'analyticità delle estremali degli integrali multipli regolari
    • E. DE GIORGI - Sulla differenziabilità e l'analyticità delle estremali degli integrali multipli regolari, Mem. Acad. Sci. Torino cl. Sci. Fis. Mat. Nat. 3 (1957), p. 25-43.
    • (1957) Mem. Acad. Sci. Torino Cl. Sci. Fis. Mat. Nat. , vol.3 , pp. 25-43
    • De Giorgi, E.1
  • 33
    • 0030602110 scopus 로고    scopus 로고
    • Semigroup kernels, Poisson bounds, and holomorphic functional calculus
    • X. DUONG and D. ROBINSON - Semigroup kernels, Poisson bounds, and holomorphic functional calculus, J. Funct. Anal. 142 (1996), no. 1, p. 89-128.
    • (1996) J. Funct. Anal. , vol.142 , Issue.1 , pp. 89-128
    • Duong, X.1    Robinson, D.2
  • 34
    • 33646917618 scopus 로고
    • A new proof of Moser's parabolic inequality via the old ideas of Nash
    • E. FABES and D. STROOCK - A new proof of Moser's parabolic inequality via the old ideas of Nash, Arch. Rat. Mech.Anal. 96 (1986), p. 327-338.
    • (1986) Arch. Rat. Mech.Anal. , vol.96 , pp. 327-338
    • Fabes, E.1    Stroock, D.2
  • 35
    • 18244429322 scopus 로고
    • Multilinear Littlewood-Paley estimates with applications to partial differential equations
    • E. FABES, D. JERISON and C. KENIG - Multilinear Littlewood-Paley estimates with applications to partial differential equations, Proc. Nat. Acad. Sci. USA 79 (1982), p. 5746-5750.
    • (1982) Proc. Nat. Acad. Sci. USA , vol.79 , pp. 5746-5750
    • Fabes, E.1    Jerison, D.2    Kenig, C.3
  • 36
    • 0001419120 scopus 로고
    • Necessary and sufficient conditions for the absolute continuity of elliptic-harmonic measure
    • _ Necessary and sufficient conditions for the absolute continuity of elliptic-harmonic measure, Ann. Math. 119 (1984), p. 121-141.
    • (1984) Ann. Math. , vol.119 , pp. 121-141
  • 37
    • 0000054569 scopus 로고
    • Square functions and partial differential equations
    • _ Square functions and partial differential equations, Amer. J. of Math. 107 (1985), p. 1325-1367.
    • (1985) Amer. J. of Math. , vol.107 , pp. 1325-1367
  • 38
    • 0003283911 scopus 로고
    • Multiple integrals in the calculus of variations and non-linear elliptic systems
    • Princeton Univ. Press
    • M. GIAQUINTA - Multiple integrals in the calculus of variations and non-linear elliptic systems, Annals of Math. Studies, vol. 105, Princeton Univ. Press, 1983.
    • (1983) Annals of Math. Studies , vol.105
    • Giaquinta, M.1
  • 39
    • 0003329538 scopus 로고
    • Introduction to regularity theory for nonlinear elliptic systems
    • Birkhauser, ETH Zürich
    • _ Introduction to regularity theory for nonlinear elliptic systems, Lectures in Mathematics, Birkhauser, ETH Zürich, 1993.
    • (1993) Lectures in Mathematics
  • 41
    • 84972551122 scopus 로고
    • A local version of the real Hardy spaces
    • D. GOLDBERG - A local version of the real Hardy spaces, Duke Math. J. 46 (1979), p. 27-42.
    • (1979) Duke Math. J. , vol.46 , pp. 27-42
    • Goldberg, D.1
  • 42
    • 0002317471 scopus 로고
    • Caractérisation de quelques espaces d'interpolation
    • P. GRISVARD - Caractérisation de quelques espaces d'interpolation, Arch. Rat. Mech.Anal. 25 (1967), p. 40-63.
    • (1967) Arch. Rat. Mech.Anal. , vol.25 , pp. 40-63
    • Grisvard, P.1
  • 43
    • 0000539082 scopus 로고
    • The Green function for uniformly elliptic equations
    • M. GRÜTER and K.-O. WIDMAN - The Green function for uniformly elliptic equations, Manuscripta Math. 37 (1982), p. 303-342.
    • (1982) Manuscripta Math. , vol.37 , pp. 303-342
    • Grüter, M.1    Widman, K.-O.2
  • 45
    • 0000443844 scopus 로고
    • Remarks on the square root problem
    • J.-L. JOURNÉ - Remarks on the square root problem, Pub. Math. 35 (1991), p. 299-321.
    • (1991) Pub. Math. , vol.35 , pp. 299-321
    • Journé, J.-L.1
  • 46
    • 84972529352 scopus 로고
    • Integration of the equation of evolution in a Banach space
    • T. KATO - Integration of the equation of evolution in a Banach space, J. Math. Soc. Japan 5 (1953), p. 208-234.
    • (1953) J. Math. Soc. Japan , vol.5 , pp. 208-234
    • Kato, T.1
  • 47
    • 84972498530 scopus 로고
    • Fractional powers of dissipative operators
    • _ Fractional powers of dissipative operators, J. Math. Soc. Japan 13 (1961), p. 246-274.
    • (1961) J. Math. Soc. Japan , vol.13 , pp. 246-274
  • 49
    • 0003307061 scopus 로고
    • Harmonic Analysis techniques for second order elliptic boundary value problems
    • AMS, Providence RI
    • C. KENIG - Harmonic Analysis techniques for second order elliptic boundary value problems, CBMS - conference lecture notes, vol. 83, AMS, Providence RI, 1995.
    • (1995) CBMS - Conference Lecture Notes , vol.83
    • Kenig, C.1
  • 50
    • 0011828024 scopus 로고
    • The Cauchy integral on lipschitz curves and the square root of second order accretive operators are the same
    • (Peral, ed.), Math. Studies, North Holland
    • C. KENIG and Y. MEYER - The Cauchy integral on lipschitz curves and the square root of second order accretive operators are the same, Recent progress in Fourier analysis (Peral, ed.), Math. Studies, vol. 111, North Holland, 1985, p. 123-145.
    • (1985) Recent Progress in Fourier Analysis , vol.111 , pp. 123-145
    • Kenig, C.1    Meyer, Y.2
  • 51
    • 0001403911 scopus 로고
    • The Neumann problem for elliptic equations with non-smooth coefficients
    • C. KENIG and J. PIPHER - The Neumann problem for elliptic equations with non-smooth coefficients, Inventiones Matematicae 113 (1993), p. 447-509.
    • (1993) Inventiones Matematicae , vol.113 , pp. 447-509
    • Kenig, C.1    Pipher, J.2
  • 52
    • 84972508297 scopus 로고
    • Espaces d'interpolation et domaines de puissances fractionnaires
    • J.-L. LIONS - Espaces d'interpolation et domaines de puissances fractionnaires, J. Math. Soc. Japan 14 (1962), p. 233-241.
    • (1962) Inventiones Matematicae , vol.14 , pp. 233-241
    • Lions, J.-L.1
  • 53
    • 0041043567 scopus 로고
    • Absence of de Giorgi-type theorems for strongly elliptic equations with complex coefficients
    • V. MAZ'YA, S. NAZAROV and B. PLAMENEVSKII - Absence of De Giorgi-type theorems for strongly elliptic equations with complex coefficients, J. Math. Sov. 28 (1985), p. 726-739.
    • (1985) J. Math. Sov. , vol.28 , pp. 726-739
    • Maz'ya, V.1    Nazarov, S.2    Plamenevskii, B.3
  • 55
    • 10244229475 scopus 로고
    • *1/2v)
    • (H. Brezis and J.-L. Lions, ed.), Research Notes in Mathematics, Pitman
    • *1/2v), Collège de France Seminar, Volume III (H. Brezis and J.-L. Lions, ed.), Research Notes in Mathematics, no. 70, Pitman, 1982, p. 252-267.
    • (1982) Collège de France Seminar, Volume III , vol.3 , Issue.70 , pp. 252-267
  • 56
    • 33748091605 scopus 로고
    • Square roots of operators and applications to hyperbolic PDE's
    • (Canberra), Center for Math. and Appl., Australian National Univ.
    • _ Square roots of operators and applications to hyperbolic PDE's, Miniconference on operator theory and partial differential equations (Canberra), Center for Math. and Appl., Australian National Univ., 1983.
    • (1983) Miniconference on Operator Theory and Partial Differential Equations
  • 57
    • 0000770482 scopus 로고
    • Square roots of elliptic operators
    • _ Square roots of elliptic operators, J. Funct. Anal. 61 (1985), p. 307-327.
    • (1985) J. Funct. Anal. , vol.61 , pp. 307-327
  • 58
    • 0001309606 scopus 로고
    • ∞ functional calculus
    • (Canberra), Center for Math. and Appl., Australian National Univ.
    • ∞ functional calculus, Miniconference on operator theory and partial differential equations (Canberra), Center for Math. and Appl., vol. 14, Australian National Univ., 1986, p. 210-231.
    • (1986) Miniconference on Operator Theory and Partial Differential Equations , vol.14 , pp. 210-231
  • 59
    • 0000462612 scopus 로고
    • Clifford algebras and the higher dimensional Cauchy integral
    • Banach Center publications, Polish Scientific Publishers
    • _ Clifford algebras and the higher dimensional Cauchy integral, Approximation and function spaces, Banach Center publications, vol. 22, Polish Scientific Publishers, 1989.
    • (1989) Approximation and Function Spaces , vol.22
  • 60
    • 0001020697 scopus 로고
    • The square root problem for elliptic operators
    • Functional analytic methods for partial differential equations (Berlin), Springer-Verlag
    • _ The square root problem for elliptic operators, Functional analytic methods for partial differential equations (Berlin), Lect. Notes in Math., vol. 1450, Springer-Verlag, 1990, p. 122-140.
    • (1990) Lect. Notes in Math. , vol.1450 , pp. 122-140
  • 61
    • 0011904727 scopus 로고
    • Algèbres d'opérateurs définis par des intégrales singulières
    • Série 1
    • A. MCINTOSH and Y. MEYER - Algèbres d'opérateurs définis par des intégrales singulières, C. R. Acad. Sci. Paris 301, Série 1 (1985), p. 395-397.
    • (1985) C. R. Acad. Sci. Paris , vol.301 , pp. 395-397
    • Mcintosh, A.1    Meyer, Y.2
  • 62
    • 0000680241 scopus 로고
    • ∞ functional calculus
    • (Canberra), Center for Math. and Appl., Australian National Univ.
    • ∞ functional calculus, Miniconference on Operators in Analysis (Canberra), Center for Math. and Appl., vol. 24, Australian National Univ., 1989, p. 159-174.
    • (1989) Miniconference on Operators in Analysis , vol.24 , pp. 159-174
    • Mcintosh, A.1    Yagi, A.2
  • 65
    • 84980080977 scopus 로고
    • On Harnack's theorem for elliptic partial differential equations
    • J. MOSER - On Harnack's theorem for elliptic partial differential equations, Comm. Pure & Appli. Math. 14 (1961), p. 577-691.
    • (1961) Comm. Pure & Appli. Math. , vol.14 , pp. 577-691
    • Moser, J.1
  • 66
    • 0001680091 scopus 로고
    • Continuity of solutions of parabolic and elliptic equations
    • J. NASH - Continuity of solutions of parabolic and elliptic equations, Amer. J. of Math. 80 (1958), p. 931-954.
    • (1958) Amer. J. of Math. , vol.80 , pp. 931-954
    • Nash, J.1
  • 67
    • 84957132367 scopus 로고
    • Two sided estimates of fundamental solutions of second order parabolic equations and some applications
    • F. PORPER and S. EIDEL'MAN - Two sided estimates of fundamental solutions of second order parabolic equations and some applications, Russian Math. Surveys 39 (1984), no. 3, p. 119-178.
    • (1984) Russian Math. Surveys , vol.39 , Issue.3 , pp. 119-178
    • Porper, F.1    Eidel'man, S.2
  • 69
    • 84968498721 scopus 로고
    • Square function estimates and the T(b) Theorem
    • S. SEMMES - Square function estimates and the T(b) Theorem, Proc. Amer. Math. Soc. 110 (1990), no. 3, p. 721-726.
    • (1990) Proc. Amer. Math. Soc. , vol.110 , Issue.3 , pp. 721-726
    • Semmes, S.1
  • 70
    • 0000212027 scopus 로고
    • Spectral properties of linear operators in interpolation families of Banach spaces
    • I. SNEIBERG - Spectral properties of linear operators in interpolation families of Banach spaces, mat. Issled. 9 (1974), p. 214-229.
    • (1974) Mat. Issled. , vol.9 , pp. 214-229
    • Sneiberg, I.1
  • 72
    • 0003520799 scopus 로고
    • Topics in harmonic analysis related to the Littlewood-Paley theory
    • Princeton Univ. Press
    • _ Topics in harmonic analysis related to the Littlewood-Paley theory, Annals of Math. Studies, vol. 63, Princeton Univ. Press, 1970.
    • (1970) Annals of Math. Studies , vol.63
  • 73
    • 84966254259 scopus 로고
    • The development of square function estimates in the work of Antoni Zygmund
    • _ The development of square function estimates in the work of Antoni Zygmund, Bull. Amer. Math. Soc. 7 (1982), p. 359-376.
    • (1982) Bull. Amer. Math. Soc. , vol.7 , pp. 359-376
  • 74
    • 0004136765 scopus 로고
    • Princeton Univ. Press
    • _ Harmonic analysis, Princeton Univ. Press, 1993.
    • (1993) Harmonic Analysis
  • 76
    • 0001402085 scopus 로고
    • Multipliers on fractional sobolev spaces
    • R. STRICHARTZ - Multipliers on fractional sobolev spaces, J. Math. Mech 16 (1967), p. 1031-1060.
    • (1967) J. Math. Mech , vol.16 , pp. 1031-1060
    • Strichartz, R.1
  • 78
    • 0000830871 scopus 로고
    • Analysis on Morrey spaces and applications to Navier-Stokes equations and other evolution equations
    • M. TAYLOR - Analysis on Morrey spaces and applications to Navier-Stokes equations and other evolution equations, Comm. Partial & Diff. Equa. 17 (1992), p. 1407-1456.
    • (1992) Comm. Partial & Diff. Equa. , vol.17 , pp. 1407-1456
    • Taylor, M.1
  • 79
    • 0003295738 scopus 로고
    • Theory of function spaces
    • Birkhauser
    • H. TRIEBEL - Theory of function spaces, Monographs in Math. vol. 78, Birkhauser, 1983.
    • (1983) Monographs in Math. , vol.78
    • Triebel, H.1
  • 81
    • 0003366040 scopus 로고
    • Coïncidence entre des espaces d'interpolation et des domaines de puissance fractionnaires d'opérateurs
    • Série 1
    • A. YAGI - Coïncidence entre des espaces d'interpolation et des domaines de puissance fractionnaires d'opérateurs, C. R. Acad. Sci. Paris 299, Série 1 (1984), p. 173-176.
    • (1984) C. R. Acad. Sci. Paris , vol.299 , pp. 173-176
    • Yagi, A.1


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