BSU Bulletin. Mathematics, Informatics
Bibliographic description:
, SOME PROBLEMS IN HÖLDER AND BESOV CLASSES // BSU Bulletin. Mathematics, Informatics. - 2020. №4. . - С. 3-13.
Title:
SOME PROBLEMS IN HÖLDER AND BESOV CLASSES
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Annotation:
In recent decades, the study of integral operators with Bergman kernels in spaces of smooth functions in complex and functional analysis has not lost its relevance. The article deals with the above-named operators in analytic spaces of the functions extended smoothly to the boundary of the domain, which boundary values belong to the Hölder and Besov classes. We have described the behavior of such operators in a circle and a half-plane. It is established that an integral operator with Bergman kernels projects Hölder classes in the case of a circle, and Besov classes in the case of a half-plane, onto the corresponding classes of analytic functions, that is, Bergman integral operator leaves the indicated classes invariant
Keywords:
integral operator; kernel; Bergman kernel; class of functions; Besov class; analytic functions; unit disc; half-plane; function space; boundary values.
List of references:
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2. Nikolsky S. M. Priblizhenie funktsii mnogikh peremennykh i teorema vlozheniya [Approximation of Functions of Several Variables and the Embedding Theorem]. Moscow: Nauka Publ., 1981. 456 p.
3. Stein E. M. Singular Integrals and Differentiability Properties of Functions. Princeton University Press, 1971, 1973. 304 p.
4. Triebel H. Theory of Function Spaces. Birkhäuser, 1983. 281 p.
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6. Shamoyan F. A., Shubabko E. N. Vvedenie v teoriyu vesovykh Lp-klassov meromorfnykh funktsii [Introduction to the Theory of Weighted Lp-Classes of Meromorphic Functions]. Bryansk: Desyatochka Publ., 2009. 153 p.
2. Nikolsky S. M. Priblizhenie funktsii mnogikh peremennykh i teorema vlozheniya [Approximation of Functions of Several Variables and the Embedding Theorem]. Moscow: Nauka Publ., 1981. 456 p.
3. Stein E. M. Singular Integrals and Differentiability Properties of Functions. Princeton University Press, 1971, 1973. 304 p.
4. Triebel H. Theory of Function Spaces. Birkhäuser, 1983. 281 p.
5. Shamoyan F. A. Diagonalnoe otobrazhenie i voprosy predstavleniya v anizotropnykh prostranstvakh golomorfnykh v polidiske funktsii [Diagonal Mapping and Problems of Representation in Anisotropic Spaces of Holomorphic Functions in the Polydisk]. Siberian Mathematical Journal. 1990. Vol. 31, no. 2. Pp. 350–365.
6. Shamoyan F. A., Shubabko E. N. Vvedenie v teoriyu vesovykh Lp-klassov meromorfnykh funktsii [Introduction to the Theory of Weighted Lp-Classes of Meromorphic Functions]. Bryansk: Desyatochka Publ., 2009. 153 p.
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