×
Mironova, S. R.; Pogodina, A. Yu.

Estimate of the norm of the singular integral operator in weighted Hölder spaces. (English) Zbl 07896209

Lobachevskii J. Math. 45, No. 3, 1207-1212 (2024).

MSC:

30E20 Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane

Keywords:

singular integral operator; weighted Hölder spaces
Cite Review PDF
Full Text: DOI

References:

[1] Muskhelishvili, N. I., Singular Integral Equations, 1953, Groningen: Noordhoff, Groningen · Zbl 0051.33203
[2] Gakhov, F. D., Boundary Value Problems, 1966, Oxford: Pergamon, Oxford · Zbl 0141.08001 · doi:10.1016/B978-0-08-010067-8.50007-4
[3] Aleksandrov, A. B., Norm of the Hilbert transformation in a space of Hölder functions, Funct. Anal. Appl., 9, 94-96, 1975 · Zbl 0318.44008 · doi:10.1007/BF01075444
[4] Paatashvili, V. A., On singular Cauchy integral on a countable set of contours, Tr. Tbilis. Mat. Inst. AN GSSR, 65, 122-130, 1980 · Zbl 0461.30034
[5] Dyn’kin, E. M., On the smoothness of Cauchy type integrals, Zap. Nauch. Sem. LOMI, 92, 115-133, 1979 · Zbl 0432.30033
[6] T. S. Salimov, ‘‘Direct estimation for the singular Cauchy integral over a closed curve,’’ Nauch. Tr. MV SSO Azerb. SSR, тДЦ 5, 59-75 (1979).
[7] M. Kh. Brenerman and B. A. Kats, ‘‘A norm estimate of a singular integral and its application to certain boundary-value problems,’’ Sov. Math. (Iz. VUZ) 29 (1), 8-18 (1985). · Zbl 0587.30039
[8] Stein, E. M., Singular Integrals and Differentiability Properties of Functions, 1970, Princeton: Princeton Univ. Press, Princeton · Zbl 0207.13501
[9] Vekua, I. N., Generalized Analytic Functions, 1962, Oxford: Pergamon, Oxford · Zbl 0127.03505
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.