Algebras of singular integral operators with piecewise continuous coefficients on reflexive Orlicz spaces

Mathematische Nachrichten

Volumn 179, Issue , 1996, Pages 187-222

  Karlovich, Aleksey Yu ^a  

^a SOUTH UKRAINIAN NATIONAL PEDAGOGICAL UNIVERSITY   (Ukraine)

Author keywords

Boyd indices; Fredholmness; Reflexive Orlicz space; Singular integral operator

Indexed keywords

EID: 0000983329     PISSN: 0025584X     EISSN: None     Source Type: Journal    
DOI: 10.1002/mana.19961790112     Document Type: Article

References (43)

1. AJZENSHTAT, A. V., KARLOVICH, YU. I.:, and LITVINCHUK, G. S.: The Method of Conformal Gluing for the Haseman Boundary Value Problem on an Open Contour, to appear
2. BENNETT, C., and SHARPLEY, R.: Interpolation of Operators, Academic Press, Boston, 1988
3. BÖTTCHER, A., and KARLOVICH, YU. I.: Toeplitz and Singular Integral Operators on Carleson Curves with Logarithmic Whirl Points, Integr. Equat. and Oper. Theory 22 (1995), 127-161
4. BÖTTCHER, A., and KARLOVICH, YU. I. Toeplitz and Singular Integral Operators on General Carleson Curves, to appear
5. BÖTTCHER, A., and SILBERMANN, B.: Analysis of Toeplitz Operators, Akademie Verlag, Berlin, 1989, and Springer Verlag, Berlin, Heidelberg, New York, 1990
6. BOYD, D. W.: Spaces between a Pair Reflexive Lebesgue Spaces, Proc. Amer. Math. Soc. 18 (1967), 215-219
7. BOYD, D. W.: The Hilbert Transform on Rearrangement-Invariant Spaces, Can. J. Math. 19 (1967), 599-616
8. BOYD, D. W.: Indices of Function Spaces and Their Relationship to Interpolation, Can. J. Math. 21 (1969), 1245-1254
9. BOYD, D. W.: Indices for the Orlicz Spaces, Pacific J. Math. 38 (1971), 315-323
10. CALDERÓN, A. P.: Intermediate Spaces and Interpolation, the Complex Method, Studia Math. 24 (1964), 113-190
11. COBURN, L. A.: Weyl's Theorem for Non-Normal Operators, Michigan Math. J. 13 (1966), 285-286
12. DAVID, G.: Operáteurs Intégraux Singuliers sur Certaines Courbes du Plan Complexe, Ann. Sci. École Norm. Super 17 (1984), 157-189
13. FINCK, T., ROCH, S., and SILBERMANN, B.: Two Projections Theorems and Symbol Calculus for Operators with Massive Local Spectra, Math. Nachr. 162 (1993), 167-185
14. GAIER, D.: Lectures on Complex Approximation, Birkhäuser Verlag, Basel, Boston, Stuttgart, 1987
15. p, Studia Math. 31 (1968), 347-362 (Russian)
16. GOHBERG, I., and KRUPNIK, N.: One-Dimensional Linear Singular Integral Equations, Vol. 1, Introduction, Birkhäuser Verlag, Basel, Boston, Berlin, 1992 (Russian original: Shtiintsa, Kishinev 1973)
17. GOHBERG, I., and KRUPNIK, N.: One-Dimensional Linear Singular Integral Equations, Vol. 2, General Theory and Applications, Birkhäuser Verlag, Basel, Boston, Berlin, 1992 (Russian original: Shtiintsa, Kishinev 1973)
18. GOHBERG, I., and KRUPNIK, N.: Extension Theorems for Fredholm and Invertibility Symbols, Integr. Equat. and Oper. Theory 17 (1993), 514-529
19. GOHBERG, I., KRUPNIK, N., and SPITKOVSKY, I.: Banach Algebras of Singular Integral Operators with Piecewise Continuous Coefficients. General Contour and Weight, Integr. Equat. and Oper. Theory 17 (1993), 322-337
20. GORDADZE, E.: On Singular Integrals with Cauchy Kernel, Trudy Tbilis. Mat. Inst. im. Razmadze Akad. Nauk Gruzin. SSR 42 (1972), 5-17 (Russian)
21. HERRERO, D.: One-Sided Interpolation of Fredholm Operators, Proc. Roy. Irish. Acad., A, 89 no. 1 (1989), 79-89
22. HUNT, R., MUCKENHOUPT, B., and WHEEDEN, R.: Weighted Norm Inequalities for the Conjugate Function and Hilbert Transform, Trans. Amer. Math. Soc. 176 (1973), 227-251
23. KARLOVICH, A. YU.: Singular Integral Operators with Piecewise Continuous Coefficients on Reflexive Orlicz Spaces, to appear
24. KARLOVICH, A. YU.: Singular Integral Operators with Regulated Coefficients on Reflexive Orlicz Spaces, to appear
25. KAZARIAN, S. S.: Integral Inequalities in Orlicz Reflexive Weighted Spaces for the Conjugate Functions, Izv. Akad. Nauk Armyan SSR. Ser. Mat., 25 (1990), 261-273 (Russian). English transi.: Sov. J. Contemp. Math. Anal., Arm. Acad. Sci. 25 (1990), 45-57
26. KAZARIAN, S. S.: Integral Inequalities in Orlicz Reflexive Weighted Spaces for the Conjugate Functions, Izv. Akad. Nauk Armyan SSR. Ser. Mat., 25 (1990), 261-273 (Russian). English transi.: Sov. J. Contemp. Math. Anal., Arm. Acad. Sci. 25 (1990), 45-57
27. KERMAN, R. A., and TORCHINSKY, A.: Integral Inequalities with Weights for the Hardy Maximal Function, Studia Math. 71 no. 3 (1982), 277-284
28. KRASNOSELSKII, M. A., and RUTITSKII, YA. B.: Convex Functions and Orlicz Spaces, Fizmatgiz, Moscow, 1958 (Russian). English transi.: Noordhoff Ltd., Groningen, 1961
29. LINDENSTRAUSS, J., and TZAFRIRI, L.: Classical Banach Spaces. Function Spaces, Springer Verlag, New York, Berlin, 1979
30. MALIGRANDA, L.: Orlicz Spaces and Interpolation, Sem. Math. 5, Dep. Mat., Univ. Estadual de Campinas, Campinas SP, Brazil, 1989
31. MATUSZEWSKA, W., and ORLICZ, W.: On Certain Properties of φ-functions, Bull. Acad. Polon. Sci., Ser. math, aster, et phys. 8 no. 7 (1960), 439-443
32. PRIVALOV, I. I. Boundary Properties of Analytic Functions, Moscow, Leningrad, GITTL, 1950 (Russian). German transi.: Randeigenschaften analytischer Funktionen, Deutscher Verlag der Wissenschaften, Berlin, 1956
33. SEIFULLAEV, R. K.: 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)
34. SEIFULLAEV, R. K.: 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)
35. SIMONENKO, I. B.: A New General Method of Studying Linear Operator Equations of the Type of Singular Integral Equations, Part 1: Izv. Akad. Nauk SSSR, Ser. Mat. 29 (1965), 567-586. Part 2: Izv. Akad. Nauk SSSR, Ser. Mat. 29 (1965), 757-782 (Russian)
36. SIMONENKO, I. B.: A New General Method of Studying Linear Operator Equations of the Type of Singular Integral Equations, Part 1: Izv. Akad. Nauk SSSR, Ser. Mat. 29 (1965), 567-586. Part 2: Izv. Akad. Nauk SSSR, Ser. Mat. 29 (1965), 757-782 (Russian)
37. SIMONENKO, I. B.: Some General Questions in the Theory of the Riemann Boundary Value Problem, Izv. Akad. Nauk SSSR, Ser. Mat. 32 (1968), 1138-1146 (Russian). English transl.: Math. USSR Izv. 2 (1968) 1091-1099
38. SIMONENKO, I. B.: Some General Questions in the Theory of the Riemann Boundary Value Problem, Izv. Akad. Nauk SSSR, Ser. Mat. 32 (1968), 1138-1146 (Russian). English transl.: Math. USSR Izv. 2 (1968) 1091-1099
39. SHNEIBERG, I. YA.: On the Solvability of Linear Equations in Interpolation Scales of Banach Spaces, Dokl. Akad. Nauk SSSR 212 (1973), 57-59 (Russian)
40. SHNEIBERG, I. YA.: Spectral Properties of Linear Operators in Interpolation Families of Banach Spaces, Mat. issled., Kishinev 9 no. 2 (1974), 214-229 (Russian)
41. SPITKOVSKY, I.: Singular Integral Operators with PC Symbols on the Spaces with General Weights, J. Funct. Analysis 105 (1992), 129-143
42. YAOHUA, D.: Singular Integral Equations in Orlicz Spaces (1), Acta Math. Sci. 3 no. 1 (1983), 71-83
43. YAOHUA, D.: Singular Integral Equations in Orlicz Spaces (2), Acta Math. Sci. 9 no. 2 (1989), 215-226