This article is cited in 3 papers

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.

UDC: 517.53

Received: 27.05.2008

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

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