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Volumn 351, Issue 8, 1999, Pages 3143-3196

Toeplitz operators with pc symbols on general Carleson Jordan curves with arbitrary Muckenhoupt weights

Author keywords

Ahlfors David curve; Carleson condition; Fredholm operator; Muckenhoupt condition; Singular integral operator; Submultiplicative function; Toeplitz operator

Indexed keywords


EID: 85009738307     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9947-99-02441-1     Document Type: Article
Times cited : (8)

References (34)
  • 1
    • 84933791782 scopus 로고
    • On the defect numbers of the Kveselava-Vekua operator with discontinuous derivative of the shift
    • MR 93d:30008
    • A. V. Aizenshtat, Yu. I. Karlovich, and G. S. Litvinchuk, On the defect numbers of the Kveselava-Vekua operator with discontinuous derivative of the shift, Soviet Math. Dokl. 43 (1991), 633-638. MR 93d:30008
    • (1991) Soviet Math. Dokl , vol.43 , pp. 633-638
    • Aizenshtat, A.V.1    Karlovich, Y.I.2    Litvinchuk, G.S.3
  • 2
    • 0039907037 scopus 로고    scopus 로고
    • The method of conformal gluing for the Haseman boundary value problem on an open contour
    • A. V. Aizenshtat, Yu. I. Karlovich, and G. S. Litvinchuk, The method of conformal gluing for the Haseman boundary value problem on an open contour, Complex Variables 28 (1996), 313-346.
    • (1996) Complex Variables , vol.28 , pp. 313-346
    • Aizenshtat, A.V.1    Karlovich, Y.I.2    Litvinchuk, G.S.3
  • 4
    • 0001145340 scopus 로고
    • Toeplitz and singular integral operators on Carleson curves with logarithmic whirl points
    • MR 96j:47022
    • A. Böttcher and Yu. I. Karlovich, Toeplitz and singular integral operators on Carleson curves with logarithmic whirl points, Integral Equations and Operator Theory 22 (1995), 127-161. MR 96j:47022
    • (1995) Integral Equations and Operator Theory , vol.22 , pp. 127-161
    • Böttcher, A.1    Karlovich, Y.I.2
  • 5
    • 0000600185 scopus 로고    scopus 로고
    • Toeplitz and singular integral operators on general Car- leson Jordan curves
    • MR 97k:47024
    • A. Böttcher and Yu. I. Karlovich, Toeplitz and singular integral operators on general Car- leson Jordan curves, Operator Theory: Advances and Applications 90 (1996), 119-152. MR 97k:47024
    • (1996) Operator Theory: Advances and Applications , vol.90 , pp. 119-152
    • Böttcher, A.1    Karlovich, Y.I.2
  • 6
    • 84966305551 scopus 로고
    • Akademie-Verlag, Berlin 1989 and Springer-Verlag, Berlin, Heidelberg, New York, MR 92e:47001
    • A. Böttcher and B. Silbermann, Analysis of Toeplitz operators, Akademie-Verlag, Berlin 1989 and Springer-Verlag, Berlin, Heidelberg, New York 1990. MR 92e:47001
    • (1990) Analysis of Toeplitz Operators
    • Böttcher, A.1    Silbermann, B.2
  • 7
    • 84972549618 scopus 로고
    • Indices for the Orlicz spaces
    • MR 46:6008
    • D. Boyd, Indices for the Orlicz spaces, Pacific J. Math. 38 (1971), 315-323. MR 46:6008
    • (1971) Pacific J. Math , vol.38 , pp. 315-323
    • Boyd, D.1
  • 8
    • 0001456769 scopus 로고
    • Weyl's theorem for non-normal operators
    • MR 34:1846
    • L. A. Coburn, Weyl's theorem for non-normal operators, Michigan Math. J. 13 (1966), 285-286. MR 34:1846
    • (1966) Michigan Math. J , vol.13 , pp. 285-286
    • Coburn, L.A.1
  • 9
    • 0039314730 scopus 로고
    • The Riemann boundary value problem on contours with unbounded distortion
    • Odessa, [Russian]
    • E. A. Danilov, The Riemann boundary value problem on contours with unbounded distortion, Cand. Dissertation, Odessa 1984 [Russian].
    • (1984) Cand. Dissertation
    • Danilov, E.A.1
  • 11
    • 0001448564 scopus 로고
    • Opérateurs intégraux singuliers sur certaines courbes du plan complexe
    • G. David, Opérateurs intégraux singuliers sur certaines courbes du plan complexe, Ann. Sci. École Norm. Super 17 (1984), 157-189.
    • (1984) Ann. Sci. École Norm. Super , vol.17 , pp. 157-189
    • David, G.1
  • 13
    • 0001129690 scopus 로고
    • Methods of the theory of singular integrals (Hilbert transform and Calderon- Zygmund theory
    • Moscow, [Russian]. CMP 20:04
    • E. M. Dynkin, Methods of the theory of singular integrals (Hilbert transform and Calderon- Zygmund theory), In: Itogi Nauki Tekh., Sovr. Probl. Matem., Fund. Napravl., vol. 15, Moscow 1987, pp. 197-292 [Russian]. CMP 20:04
    • (1987) Itogi Nauki Tekh., Sovr. Probl. Matem., Fund. Napravl , vol.15 , pp. 197-292
    • Dynkin, E.M.1
  • 14
    • 0037527572 scopus 로고
    • Methods of the theory of singular integrals II (Littlewood-Paley theory and its applications)
    • Moscow, RussianMR 91j:42015
    • E. M. Dynkin, Methods of the theory of singular integrals II (Littlewood-Paley theory and its applications), In: Itogi Nauki Tekh., Sovr. Probl. Matem., Fund. Napravl., vol. 42, Moscow 1989, pp. 105-198 [Russian]. MR 91j:42015
    • (1989) Itogi Nauki Tekh., Sovr. Probl. Matem., Fund. Napravl , vol.42 , pp. 105-198
    • Dynkin, E.M.1
  • 15
    • 34250118364 scopus 로고
    • Weighted norm estimates for singular integrals and their applications
    • [Russian original: Itogi Nauki Tekh., Ser. Mat. Anal. 21 (1983), 42-129]
    • E. M. Dynkin and B. P. Osilenker, Weighted norm estimates for singular integrals and their applications, J. Sov. Math. 30 (1985), 2094-2154 [Russian original: Itogi Nauki Tekh., Ser. Mat. Anal. 21 (1983), 42-129].
    • (1985) J. Sov. Math , vol.30 , pp. 2094-2154
    • Dynkin, E.M.1    Osilenker, B.P.2
  • 16
    • 0001234210 scopus 로고
    • Two projections theorems and symbol calculus for operators with massive local spectra
    • MR 94h:47083
    • T. Finck, S. Roch, and B. Silbermann, Two projections theorems and symbol calculus for operators with massive local spectra, Math. Nachr. 162 (1993), 167-185. MR 94h:47083
    • (1993) Math. Nachr , vol.162 , pp. 167-185
    • Finck, T.1    Roch, S.2    Silbermann, B.3
  • 18
    • 0013036078 scopus 로고
    • On an application of the theory of normed rings to singular integral equations
    • [Russian]MR 14:54a
    • I. Gohberg, On an application of the theory of normed rings to singular integral equations, Uspehi Matem. Nauk 7 (1952), 149-156 [Russian]. MR 14:54a
    • (1952) Uspehi Matem. Nauk , vol.7 , pp. 149-156
    • Gohberg, I.1
  • 19
    • 0000079021 scopus 로고
    • Singular integral operators with piecewise continuous coefficients and their symbols
    • I. Gohberg and N. Krupnik, Singular integral operators with piecewise continuous coefficients and their symbols, Math. USSR Izv. 5 (1971), 955-979.
    • (1971) Math. USSR Izv , vol.5 , pp. 955-979
    • Gohberg, I.1    Krupnik, N.2
  • 20
    • 85009830958 scopus 로고
    • Birkhäuser Verlag, Basel, Boston, Berlin 1992 [Russian original: Shtiintsa, Kishinev
    • I. Gohberg and N. Krupnik, One-dimensional linear singular integral equations, Vols. I and II, Birkhäuser Verlag, Basel, Boston, Berlin 1992 [Russian original: Shtiintsa, Kishinev 1973].
    • (1973) One-Dimensional Linear Singular Integral Equations , vol.1-2
    • Gohberg, I.1    Krupnik, N.2
  • 21
    • 0000255519 scopus 로고
    • Extension theorems for Fredholm and invertibility symbols
    • I. Gohberg and N. Krupnik, Extension theorems for Fredholm and invertibility symbols, Integral Equations and Operator Theory 16 (1993), 514-529.
    • (1993) Integral Equations and Operator Theory , vol.16 , pp. 514-529
    • Gohberg, I.1    Krupnik, N.2
  • 22
    • 0000987655 scopus 로고
    • Banach algebras of singular integral operators with piecewise continuous coefficients, General contour and weight
    • MR 94f:47057
    • I. Gohberg, N. Krupnik, and I. M. Spitkovsky, Banach algebras of singular integral operators with piecewise continuous coefficients, General contour and weight. Integral Equations and Operator Theory 17 (1993), 322-337. MR 94f:47057
    • (1993) Integral Equations and Operator Theory , vol.17 , pp. 322-337
    • Gohberg, I.1    Krupnik, N.2    Spitkovsky, I.M.3
  • 23
    • 0003230949 scopus 로고
    • Functional analysis and semi-groups
    • revised edition, Providence, R.I
    • E. Hille and R. S. Phillips, Functional analysis and semi-groups, Amer. Math. Soc. Coll. Publ., vol. 31, revised edition, Providence, R.I, 1957.
    • (1957) Amer. Math. Soc. Coll. Publ , vol.31
    • Hille, E.1    Phillips, R.S.2
  • 24
    • 84968496736 scopus 로고
    • Weighted norm inequalities for the conjugate function and Hilbert transform
    • MR 47:701
    • R. Hunt, B. Muckenhoupt, and R. Wheeden, Weighted norm inequalities for the conjugate function and Hilbert transform, Trans. Amer. Math. Soc. 176 (1973), 227-251. MR 47:701
    • (1973) Trans. Amer. Math. Soc , vol.176 , pp. 227-251
    • Hunt, R.1    Muckenhoupt, B.2    Wheeden, R.3
  • 25
    • 0003479641 scopus 로고
    • Interpolation of linear operators
    • Providence, R.I, Russian original: Nauka, Moscow, MR 84j:46103
    • S. G. Krein, Yu. I. Petunin, and E. M. Semenov, Interpolation of linear operators, Transl. Math. Monogr. 54, Amer. Math. Soc., Providence, R.I., 1982 [Russian original: Nauka, Moscow, 1978]. MR 84j:46103
    • (1982) Transl. Math. Monogr. 54, Amer. Math. Soc
    • Krein, S.G.1    Petunin, Y.I.2    Semenov, E.M.3
  • 26
    • 0011286867 scopus 로고
    • On the boundedness of the Cauchy singular integral on Lebesgue spaces in the case of non-smooth contours
    • Russian
    • V. A. Paatashvili and G. A. Khuskivadze, On the boundedness of the Cauchy singular integral on Lebesgue spaces in the case of non-smooth contours, Trudy Tbilisk. Mat. Inst. AN GSSR 69 (1982), 93-107 [Russian].
    • (1982) Trudy Tbilisk. Mat. Inst. AN GSSR , vol.69 , pp. 93-107
    • Paatashvili, V.A.1    Khuskivadze, G.A.2
  • 27
    • 0004267646 scopus 로고
    • Princeton University Press, Princeton, MR 43:445
    • R. T. Rockafellar, Convex analysis, Princeton University Press, Princeton 1970. MR 43:445
    • (1970) Convex Analysis
    • Rockafellar, R.T.1
  • 28
    • 0013532724 scopus 로고
    • The Riemann boundary value problem on non-smooth open curves
    • [Russian] (English transl. in Math. USSR Sb. 40 (1981))
    • R. K. Seifullayev, The Riemann boundary value problem on non-smooth open curves, Matem. Sb. 112 (1980), 147-161 [Russian] (English transl. in Math. USSR Sb. 40 (1981)).
    • (1980) Matem. Sb , vol.112 , pp. 147-161
    • Seifullayev, R.K.1
  • 29
    • 0002249297 scopus 로고
    • The Riemann boundary value problem with measurable coefficients
    • Russian
    • I. B. Simonenko, The Riemann boundary value problem with measurable coefficients, Dokl. Akad. Nauk SSSR 135 (1960), 538-541 [Russian].
    • (1960) Dokl. Akad. Nauk SSSR , vol.135 , pp. 538-541
    • Simonenko, I.B.1
  • 30
    • 0000372339 scopus 로고
    • Some general questions of the theory of the Riemann boundary value problem
    • I. B. Simonenko, Some general questions of the theory of the Riemann boundary value problem, Math. USSR Izv. 2 (1968), 1091-1099.
    • (1968) Math. USSR Izv , vol.2 , pp. 1091-1099
    • Simonenko, I.B.1
  • 31
    • 0001147632 scopus 로고
    • On the factorization and local factorization of measurable functions
    • I. B. Simonenko, On the factorization and local factorization of measurable functions, Soviet Math. Dokl. 21 (1980), 271-274.
    • (1980) Soviet Math. Dokl , vol.21 , pp. 271-274
    • Simonenko, I.B.1
  • 32
    • 84892052204 scopus 로고
    • Stability of weight properties of functions with respect to the singular integral
    • Russian
    • I. B. Simonenko, Stability of weight properties of functions with respect to the singular integral, Matem. Zametki 33 (1983), 409-416 [Russian].
    • (1983) Matem. Zametki , vol.33 , pp. 409-416
    • Simonenko, I.B.1
  • 33
    • 0000453429 scopus 로고
    • Singular integral operators with PC symbols on the spaces with general weights
    • MR 93d:47057
    • I. M. Spitkovsky, Singular integral operators with PC symbols on the spaces with general weights, J. Funct. Anal. 105 (1992), 129-143. MR 93d:47057
    • (1992) J. Funct. Anal , vol.105 , pp. 129-143
    • Spitkovsky, I.M.1
  • 34
    • 84968475664 scopus 로고
    • Singular integral equations in Lp
    • MR 22:9830
    • H. Widom, Singular integral equations in Lp, Trans. Amer. Math. Soc. 97 (1960), 131-160. MR 22:9830
    • (1960) Trans. Amer. Math. Soc , vol.97 , pp. 131-160
    • Widom, H.1


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