This article is cited 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.

UDC: 517.53

Received: 28.12.2010

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

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