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Sibirsk. Mat. Zh., 2012, Volume 53, Number 3, Pages 691–711 (Mi smj2356)  

This article is cited in 1 scientific paper (total in 1 paper)

A boundedness criterion for Toeplitz operators in weighted Sobolev spaces of holomorphic functions on the polydisk

F. A. Shamoyan

Bryansk State University, Bryansk

Abstract: We obtain a full description of the summable functions $h$ on the torus which admit pluriharmonic continuation to the unit polydisk for which the Toeplitz operator with symbol $h$ is a bounded operator in the weighted Sobolev spaces of holomorphic functions.

Keywords: unit torus, holomorphic function, Sobolev space, Toeplitz operator, harmonic function.

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English version:
Siberian Mathematical Journal, 2012, 53:3, 554–572

Bibliographic databases:

UDC: 517.53
Received: 28.12.2010

Citation: F. A. Shamoyan, “A boundedness criterion for Toeplitz operators in weighted Sobolev spaces of holomorphic functions on the polydisk”, Sibirsk. Mat. Zh., 53:3 (2012), 691–711; Siberian Math. J., 53:3 (2012), 554–572

Citation in format AMSBIB
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\paper A boundedness criterion for Toeplitz operators in weighted Sobolev spaces of holomorphic functions on the polydisk
\jour Sibirsk. Mat. Zh.
\yr 2012
\vol 53
\issue 3
\pages 691--711
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\jour Siberian Math. J.
\yr 2012
\vol 53
\issue 3
\pages 554--572
\crossref{https://doi.org/10.1134/S003744661202036X}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. F. A. Shamoyan, V. A. Bednazh, “Teplitsevy operatory v sobolevykh prostranstvakh analiticheskikh funktsii i ikh prilozheniya”, Sib. elektron. matem. izv., 14 (2017), 163–177  mathnet  crossref
  • Сибирский математический журнал Siberian Mathematical Journal
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