메뉴 건너뛰기




Volumn 259, Issue 2, 2010, Pages 384-427

Hardy spaces of the conjugate Beltrami equation

Author keywords

Conjugate Beltrami equation; Hardy spaces; Non tangential maximal function; Trace

Indexed keywords


EID: 77952545831     PISSN: 00221236     EISSN: 10960783     Source Type: Journal    
DOI: 10.1016/j.jfa.2010.04.004     Document Type: Article
Times cited : (28)

References (62)
  • 1
    • 84956108787 scopus 로고
    • Analytic properties of Schmidt pairs for a Hankel operator and the generalized Schur-Takagi problem
    • Adamjan V.M., Arov D.Z., Krein M.G. Analytic properties of Schmidt pairs for a Hankel operator and the generalized Schur-Takagi problem. Math. USSR Sbornik 1971, 15:31-73.
    • (1971) Math. USSR Sbornik , vol.15 , pp. 31-73
    • Adamjan, V.M.1    Arov, D.Z.2    Krein, M.G.3
  • 3
    • 0004142899 scopus 로고
    • Wadsworth and Brooks/Cole Advanced Books and Software, Monterey, CA
    • Ahlfors L. Lectures on Quasiconformal Mappings 1987, Wadsworth and Brooks/Cole Advanced Books and Software, Monterey, CA.
    • (1987) Lectures on Quasiconformal Mappings
    • Ahlfors, L.1
  • 4
    • 0003032922 scopus 로고
    • Some extremal problems linked with identification from partial frequency data
    • Springer-Verlag, J.L. Lions, R.F. Curtain, A. Bensoussan (Eds.) 10th Conference in Analysis and Optimization of Systems
    • Alpay D., Baratchart L., Leblond J. Some extremal problems linked with identification from partial frequency data. Lecture Notes in Control and Inform. Sci. 1993, vol. 185:563-573. Springer-Verlag. J.L. Lions, R.F. Curtain, A. Bensoussan (Eds.).
    • (1993) Lecture Notes in Control and Inform. Sci. , vol.185 , pp. 563-573
    • Alpay, D.1    Baratchart, L.2    Leblond, J.3
  • 5
    • 0002221589 scopus 로고
    • Area distortion of quasi-conformal mappings
    • Astala K. Area distortion of quasi-conformal mappings. Acta Math. 1994, 173:37-60.
    • (1994) Acta Math. , vol.173 , pp. 37-60
    • Astala, K.1
  • 6
    • 84883906715 scopus 로고    scopus 로고
    • Elliptic Partial Differential Equations and Quasiconformal Mappings in the Plane
    • Princeton Univ. Press
    • Astala K., Iwaniec T., Martin G. Elliptic Partial Differential Equations and Quasiconformal Mappings in the Plane. Princeton Math. Ser. 2008, Princeton Univ. Press.
    • (2008) Princeton Math. Ser.
    • Astala, K.1    Iwaniec, T.2    Martin, G.3
  • 7
    • 30444450433 scopus 로고    scopus 로고
    • Calderón's inverse conductivity problem in the plane
    • Astala K., Päivärinta L. Calderón's inverse conductivity problem in the plane. Ann. of Math. (2) 2006, 16(1):265-299.
    • (2006) Ann. of Math. (2) , vol.16 , Issue.1 , pp. 265-299
    • Astala, K.1    Päivärinta, L.2
  • 8
    • 36348940659 scopus 로고    scopus 로고
    • A boundary integral equation for Calderón's inverse conductivity problem
    • Proc. 7th Int. Conf. on Harmonic Analysis and PDEs
    • Astala K., Päivärinta L. A boundary integral equation for Calderón's inverse conductivity problem. Collect. Math. 2006, 127-139.
    • (2006) Collect. Math. , pp. 127-139
    • Astala, K.1    Päivärinta, L.2
  • 9
    • 77952099177 scopus 로고    scopus 로고
    • Bounded extremal and Cauchy Laplace problems on the sphere and shell
    • Atfeh B., Baratchart L., Leblond J., Partington J.R. Bounded extremal and Cauchy Laplace problems on the sphere and shell. J. Fourier Anal. Appl. 2010, 16(2):177-203. 10.1007/s00041-009-9110-0.
    • (2010) J. Fourier Anal. Appl. , vol.16 , Issue.2 , pp. 177-203
    • Atfeh, B.1    Baratchart, L.2    Leblond, J.3    Partington, J.R.4
  • 10
    • 0041733807 scopus 로고    scopus 로고
    • Observations on W1,p estimates for divergence elliptic equations with VMO coefficients
    • Auscher P., Qafsaoui M. Observations on W1,p estimates for divergence elliptic equations with VMO coefficients. Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. (8) 2002, 5(2):487-509.
    • (2002) Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. (8) , vol.5 , Issue.2 , pp. 487-509
    • Auscher, P.1    Qafsaoui, M.2
  • 11
    • 13744261500 scopus 로고    scopus 로고
    • Recovery of pointwise sources or small inclusions in 2D domains and rational approximation
    • Baratchart L., Ben Abda A., Ben Hassen F., Leblond J. Recovery of pointwise sources or small inclusions in 2D domains and rational approximation. Inverse Problems 2005, 21:51-74.
    • (2005) Inverse Problems , vol.21 , pp. 51-74
    • Baratchart, L.1    Ben Abda, A.2    Ben Hassen, F.3    Leblond, J.4
  • 12
    • 0037258472 scopus 로고    scopus 로고
    • Asymptotic estimates for interpolation and constrained approximation in H2 by diagonalization of Toeplitz operators
    • Baratchart L., Grimm J., Leblond J., Partington J.R. Asymptotic estimates for interpolation and constrained approximation in H2 by diagonalization of Toeplitz operators. Integral Equations Operator Theory 2003, 45:269-299.
    • (2003) Integral Equations Operator Theory , vol.45 , pp. 269-299
    • Baratchart, L.1    Grimm, J.2    Leblond, J.3    Partington, J.R.4
  • 13
    • 0002068643 scopus 로고    scopus 로고
    • Hardy approximation to Lp functions on subsets of the circle with 1p<∞
    • Baratchart L., Leblond J. Hardy approximation to Lp functions on subsets of the circle with 1p<∞. Constr. Approx. 1998, 14:41-56.
    • (1998) Constr. Approx. , vol.14 , pp. 41-56
    • Baratchart, L.1    Leblond, J.2
  • 14
    • 0001862962 scopus 로고    scopus 로고
    • How can the meromorphic approximation help to solve some 2D inverse problems for the Laplacian?
    • Baratchart L., Leblond J., Mandréa F., Saff E.B. How can the meromorphic approximation help to solve some 2D inverse problems for the Laplacian?. Inverse Problems 1999, 15:79-90.
    • (1999) Inverse Problems , vol.15 , pp. 79-90
    • Baratchart, L.1    Leblond, J.2    Mandréa, F.3    Saff, E.B.4
  • 15
    • 0000285261 scopus 로고    scopus 로고
    • Hardy approximation to L∞ functions on subsets of the circle
    • Baratchart L., Leblond J., Partington J.R. Hardy approximation to L∞ functions on subsets of the circle. Constr. Approx. 1996, 12:423-436.
    • (1996) Constr. Approx. , vol.12 , pp. 423-436
    • Baratchart, L.1    Leblond, J.2    Partington, J.R.3
  • 16
    • 0034343543 scopus 로고    scopus 로고
    • Problems of Adamjan-Arov-Krein type on subsets of the circle and minimal norm extensions
    • Baratchart L., Leblond J., Partington J.R. Problems of Adamjan-Arov-Krein type on subsets of the circle and minimal norm extensions. Constr. Approx. 2000, 16:333-357.
    • (2000) Constr. Approx. , vol.16 , pp. 333-357
    • Baratchart, L.1    Leblond, J.2    Partington, J.R.3
  • 18
    • 33745728254 scopus 로고    scopus 로고
    • 2-D inverse problems for the Laplacian: a meromorphic approximation approach
    • Baratchart L., Mandréa F., Saff E.B., Wielonsky F. 2-D inverse problems for the Laplacian: a meromorphic approximation approach. J. Math. Pures Appl. 2006, 86:1-41.
    • (2006) J. Math. Pures Appl. , vol.86 , pp. 1-41
    • Baratchart, L.1    Mandréa, F.2    Saff, E.B.3    Wielonsky, F.4
  • 19
    • 0037053173 scopus 로고    scopus 로고
    • An Lp analog to the AAK theory
    • Baratchart L., Seyfert F. An Lp analog to the AAK theory. J. Funct. Anal. 2002, 191:52-122.
    • (2002) J. Funct. Anal. , vol.191 , pp. 52-122
    • Baratchart, L.1    Seyfert, F.2
  • 20
    • 0002587885 scopus 로고
    • On a representation theorem for linear elliptic systems with discontinuous coefficients and its applications
    • Cremonese, Roma
    • Bers L., Nirenberg L. On a representation theorem for linear elliptic systems with discontinuous coefficients and its applications. Convegno Internazionale Sulle Equazioni Derivate e Parziali 1954, 111-138. Cremonese, Roma.
    • (1954) Convegno Internazionale Sulle Equazioni Derivate e Parziali , pp. 111-138
    • Bers, L.1    Nirenberg, L.2
  • 21
    • 77952548613 scopus 로고
    • Numerical Simulation and Optimal Control in Plasma Physics: With Applications to Tokamaks
    • John Wiley & Sons
    • Blum J. Numerical Simulation and Optimal Control in Plasma Physics: With Applications to Tokamaks. Modern Appl. Math. 1989, John Wiley & Sons.
    • (1989) Modern Appl. Math.
    • Blum, J.1
  • 22
    • 0000528446 scopus 로고
    • Homeomorphic solutions of Beltrami systems
    • Bojarski B. Homeomorphic solutions of Beltrami systems. Dokl. Akad. Nauk SSSR 1955, 102:661-664.
    • (1955) Dokl. Akad. Nauk SSSR , vol.102 , pp. 661-664
    • Bojarski, B.1
  • 23
    • 0005515888 scopus 로고
    • A remark on gradients of harmonic functions in dimension d3
    • Bourgain J., Wolff T. A remark on gradients of harmonic functions in dimension d3. Colloq. Math. 1990, 60/61:253-260.
    • (1990) Colloq. Math. , pp. 253-260
    • Bourgain, J.1    Wolff, T.2
  • 25
    • 0004067881 scopus 로고
    • Selected Problems in Exceptional Sets
    • Princeton
    • Carleson L. Selected Problems in Exceptional Sets. Van Nostrand Math. Stud. 1967, vol. 13. Princeton.
    • (1967) Van Nostrand Math. Stud. , vol.13
    • Carleson, L.1
  • 26
    • 1642370722 scopus 로고    scopus 로고
    • Approximation in reflexive Banach spaces and applications to the invariant subspace problem
    • Chalendar I., Partington J.R., Smith M. Approximation in reflexive Banach spaces and applications to the invariant subspace problem. Proc. Amer. Math. Soc. 2004, 132:1133-1142.
    • (2004) Proc. Amer. Math. Soc. , vol.132 , pp. 1133-1142
    • Chalendar, I.1    Partington, J.R.2    Smith, M.3
  • 27
    • 60149099952 scopus 로고    scopus 로고
    • Beltrami equations with coefficients in the Sobolev space W1,p
    • Clop A., Faraco D., Mateu J., Orobitg J., Zhong X. Beltrami equations with coefficients in the Sobolev space W1,p. Publ. Mat. 2009, 53(1):197-230.
    • (2009) Publ. Mat. , vol.53 , Issue.1 , pp. 197-230
    • Clop, A.1    Faraco, D.2    Mateu, J.3    Orobitg, J.4    Zhong, X.5
  • 28
    • 0002935719 scopus 로고
    • Solutions de l'équation de Beltrami avec {norm of matrix}μ{norm of matrix}∞=1
    • David G. Solutions de l'équation de Beltrami avec {norm of matrix}μ{norm of matrix}∞=1. Ann. Acad. Sci. Fenn. Ser. A1 Math. 1988, 13:25-70.
    • (1988) Ann. Acad. Sci. Fenn. Ser. A1 Math. , vol.13 , pp. 25-70
    • David, G.1
  • 30
    • 0003303950 scopus 로고
    • Theory of Hp Spaces
    • Academic Press, New York, London
    • Duren P.L. Theory of Hp Spaces. Pure Appl. Math. 1970, vol. 38. Academic Press, New York, London.
    • (1970) Pure Appl. Math. , vol.38
    • Duren, P.L.1
  • 31
    • 51249180564 scopus 로고
    • Potential techniques for boundary value problems on C1 domains
    • Fabes E., Jodeit M., Rivière N. Potential techniques for boundary value problems on C1 domains. Acta Math. 1978, 141:165-186.
    • (1978) Acta Math. , vol.141 , pp. 165-186
    • Fabes, E.1    Jodeit, M.2    Rivière, N.3
  • 32
    • 0003349829 scopus 로고
    • Lectures on Riemann Surfaces
    • Springer
    • Forster O. Lectures on Riemann Surfaces. Grad. Texts in Math. 1981, vol. 81. Springer.
    • (1981) Grad. Texts in Math. , vol.81
    • Forster, O.1
  • 33
    • 0002872733 scopus 로고
    • Bounded Analytic Functions
    • Academic Press
    • Garnett J. Bounded Analytic Functions. Pure Appl. Math. 1981, vol. 96. Academic Press.
    • (1981) Pure Appl. Math. , vol.96
    • Garnett, J.1
  • 35
    • 0021441691 scopus 로고
    • All optimal Hankel-norm approximations of linear multivariable systems and their L∞-error bounds
    • Glover K. All optimal Hankel-norm approximations of linear multivariable systems and their L∞-error bounds. Internat. J. Control 1984, 39(6):1115-1193.
    • (1984) Internat. J. Control , vol.39 , Issue.6 , pp. 1115-1193
    • Glover, K.1
  • 39
    • 67349264352 scopus 로고    scopus 로고
    • What's new for the Beltrami equation?
    • National Research Symposium on Geometric Analysis and Applications
    • Iwaniec T., Martin G. What's new for the Beltrami equation?. Proc. Centre Math. Appl. 2000, vol. 39.
    • (2000) Proc. Centre Math. Appl. , vol.39
    • Iwaniec, T.1    Martin, G.2
  • 43
    • 68249139907 scopus 로고    scopus 로고
    • Robust numerical algorithms based on analytic approximation for the solution of inverse problems in annular domains
    • Jaoua M., Leblond J., Mahjoub M., Partington J.R. Robust numerical algorithms based on analytic approximation for the solution of inverse problems in annular domains. IMA J. Appl. Math. 2009, 74:481-506. 10.1093/imamat/hxn041.
    • (2009) IMA J. Appl. Math. , vol.74 , pp. 481-506
    • Jaoua, M.1    Leblond, J.2    Mahjoub, M.3    Partington, J.R.4
  • 44
    • 0002814972 scopus 로고
    • Boundary value problems on Lipschitz domains
    • Amer. Math. Soc. Studies in Partial Differential Equations
    • Jerison D., Kenig C. Boundary value problems on Lipschitz domains. MAA Stud. Math. 1982, vol. 23:1-68. Amer. Math. Soc.
    • (1982) MAA Stud. Math. , vol.23 , pp. 1-68
    • Jerison, D.1    Kenig, C.2
  • 45
    • 0002796172 scopus 로고
    • Approximation of L2(ω1,ω2) functions by minimum-energy transfer functions of linear systems
    • (English transl.)
    • Krein M.G., Nudel'man P.Y. Approximation of L2(ω1,ω2) functions by minimum-energy transfer functions of linear systems. Problemy Peredachi Informatsii 1975, 11(2):37-60. (English transl.).
    • (1975) Problemy Peredachi Informatsii , vol.11 , Issue.2 , pp. 37-60
    • Krein, M.G.1    Nudel'man, P.Y.2
  • 48
    • 84972506658 scopus 로고
    • Existence of various boundary limits of Beppo Levi functions of higher order
    • Mizuta Y. Existence of various boundary limits of Beppo Levi functions of higher order. Hiroshima Math. J. 1979, 9:717-745.
    • (1979) Hiroshima Math. J. , vol.9 , pp. 717-745
    • Mizuta, Y.1
  • 49
    • 0001691124 scopus 로고
    • On the solutions of quasi-linear elliptic partial differential equations
    • Morrey C.B. On the solutions of quasi-linear elliptic partial differential equations. Trans. Amer. Math. Soc. 1938, 43(1):126-166.
    • (1938) Trans. Amer. Math. Soc. , vol.43 , Issue.1 , pp. 126-166
    • Morrey, C.B.1
  • 50
    • 0003258026 scopus 로고
    • Treatise on the Shift Operator
    • Springer
    • Nikolskii N.K. Treatise on the Shift Operator. Grundlehren Math. Wiss. 1986, vol. 273. Springer.
    • (1986) Grundlehren Math. Wiss. , vol.273
    • Nikolskii, N.K.1
  • 51
    • 4644343525 scopus 로고    scopus 로고
    • Operators, Functions, and Systems: an Easy Reading
    • Amer. Math. Soc.
    • Nikolskii N.K. Operators, Functions, and Systems: an Easy Reading. Math. Surveys Monogr. 2002, Amer. Math. Soc., pp. 92-93.
    • (2002) Math. Surveys Monogr. , pp. 92-93
    • Nikolskii, N.K.1
  • 52
    • 0000256915 scopus 로고
    • Estimates of the singular numbers of a Carleson operator
    • Parfenov O.G. Estimates of the singular numbers of a Carleson operator. Math. USSR Sbornik 1988, 59(2):497-514.
    • (1988) Math. USSR Sbornik , vol.59 , Issue.2 , pp. 497-514
    • Parfenov, O.G.1
  • 55
    • 0036077858 scopus 로고    scopus 로고
    • On Lp-generalization of a theorem of Adamjan, Arov, and Krein
    • Prokhorov V.A. On Lp-generalization of a theorem of Adamjan, Arov, and Krein. J. Approx. Theory 2002, 116(2):380-396.
    • (2002) J. Approx. Theory , vol.116 , Issue.2 , pp. 380-396
    • Prokhorov, V.A.1
  • 56
    • 17444388654 scopus 로고
    • Boundary behaviour of functions with generalized derivatives
    • Resetnyak Yu.G. Boundary behaviour of functions with generalized derivatives. Siberian Math. J. 1972, 13:285-290.
    • (1972) Siberian Math. J. , vol.13 , pp. 285-290
    • Resetnyak, Y.1
  • 58
    • 0042195884 scopus 로고    scopus 로고
    • Extraction of coupling parameters for microwave filters: Determination of a stable rational model from scattering data, in: Proceedings of the International Microwave Symposium, Philadelphia
    • F. Seyfert, J.P. Marmorat, L. Baratchart, S. Bila, J. Sombrin, Extraction of coupling parameters for microwave filters: Determination of a stable rational model from scattering data, in: Proceedings of the International Microwave Symposium, Philadelphia, 2003.
    • (2003)
    • Seyfert, F.1    Marmorat, J.P.2    Baratchart, L.3    Bila, S.4    Sombrin, J.5
  • 62
    • 0003320023 scopus 로고
    • Weakly Differentiable Functions
    • Springer-Verlag, New York
    • Ziemer W.P. Weakly Differentiable Functions. Grad. Texts in Math. 1989, vol. 120. Springer-Verlag, New York.
    • (1989) Grad. Texts in Math. , vol.120
    • Ziemer, W.P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.