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Sibirsk. Mat. Zh., 2009, Volume 50, Number 6, Pages 1413–1432 (Mi smj2060)  

A weak invertibility criterion in the weighted $L^p$-spaces of holomorphic functions in the ball

F. A. Shamoyan

Bryansk State University, Bryansk

Abstract: We obtain a necessary and sufficient condition on a weight function for every nowhere vanishing holomorphic function in the unit ball in the weighted $L^p$-space to be weakly invertible in the corresponding $L^q$-space for all $q<p$.

Keywords: weak invertibility, cyclic elements, holomorphic function, Bergman space, shift operator, weighted polynomial approximation.

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English version:
Siberian Mathematical Journal, 2009, 50:6, 1115–1132

Bibliographic databases:

UDC: 517.53
Received: 27.05.2008

Citation: F. A. Shamoyan, “A weak invertibility criterion in the weighted $L^p$-spaces of holomorphic functions in the ball”, Sibirsk. Mat. Zh., 50:6 (2009), 1413–1432; Siberian Math. J., 50:6 (2009), 1115–1132

Citation in format AMSBIB
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\pages 1413--1432
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