Submultiplicative functions and spectral theory of Toeplitz operators

Integral Transforms and Special Functions

Volumn 4, Issue 1-2, 1996, Pages 181-202

  Böttcher, Albrecht ^a   Karlovich, Yuri I ^b  

^a CHEMNITZ UNIVERSITY OF TECHNOLOGY   (Germany)

^b INSTITUTE OF HYDROBIOLOGY   (Ukraine)

Author keywords

Ahlfors David curves; Muckenhoupt condition; Singular integrals; Submultiplicative functions; Toeplitz operators

Indexed keywords

EID: 3042989154     PISSN: 10652469     EISSN: None     Source Type: Journal    
DOI: 10.1080/10652469608819105     Document Type: Review

References (26)

1. C. Bennett and R. Sharpley, Interpolation of Operators, Academic Press, Boston 1988.
2. 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.
3. A. Böttcher and Yu.I. Karlovich, Toeplitz and singular integral operators on general Carleson Jordan curves (in Press).
4. A. Böttcher and Yu.I. Karlovich, Toeplitz operators with PC symbols on general Carleson Jordan curves with arbitrary Muckenhoupt weights (in Press).
5. A. Böttcher and B. Silbermann, Analysis of Toeplitz Operators, Akademie-Verlag, Berlin 1989 and Springer-Verlag, Berlin, Heidelberg, New York 1990.
6. D. Boyd, Indices for the Orlicz spaces, Pacific J. Math. 38 (1971), 315-323.
7. A.P. Calderón, Cauchy integrals on Lipschitz curves and related operators, Proc. Nat. Acad. Sci. USA 74 (1977), 1324-1327.
8. E.A. Danilov, The Riemann boundary value problem on contours with unbounded distortion, Cand. Dissertation, Odessa 1984 (in Russian).
9. G. David, L'intégrale de Cauchy sur le courbes rectifiables, Prepublication Univ. Paris-Sud, Dept. Math. 82T05, 1982.
10. G. David, Opérateurs intégraux singuliers sur certaines courbes du plan complexe, Ann. Sci. École Norm. Super. 17 (1984), 157-189.
11. R.G. Douglas, Banach Algebra Techniques in Operator Theory Academic Press, New York 1972.
12. 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].
13. 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].
14. I. Gohberg, On an application of the theory of normed rings to singular integral equations, Uspehi Matem. Nauk 7 (1952), 149-156 (in Russian).
15. p, Studia Math. 31 (1968), 347-362 (in Russian).
16. I. Gohberg and N. Krupnik, Singular integral operators with piecewise continuous coefficients and their symbols, Math. USSR Izv. 5 (1971), 955-979.
17. I. Gohberg and N. Krupnik, One-Dimensional Linear Singular Integral Equations, I and II, Birkhäuser Verlag, Basel, Boston, Berlin 1992 [Russian original, Shtiintsa, Kishinev 1973].
18. E. Hille and R.S. Phillips, Functional Analysis and Semigroups, Amer. Math. Soc. Coll. Publ., 31, revised edition, Providence, R.I, 1957.
19. 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.
20. 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].
21. 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 (in Russian).
22. I.B. Simonenko, The Riemann boundary value problem with measurable coefficients, Dokl. Akad. Nauk SSSR 135 (1960), 538-541 (in Russian).
23. I.B. Simonenko, Some general questions of the theory of the Riemann boundary value problem, Math. USSR Izv. 2 (1968), 1091-1099.
24. I.B. Simonenko, On the factorization and local factorization of measurable functions, Soviet Math. Dokl. 21 (1980), 271-274.
25. I.M. Spitkovsky, Singular integral operators with PC symbols on the spaces with general weights, J. Funct. Anal. 105 (1992), 129-143.
26. p, Trans. Amer. Math. Soc. 97 (1960), 131-160.