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Some weighted estimates for the ∂̅-equation and a finite rank theorem for Toeplitz operators in the Fock space

Journal article
Authors Grigori Rozenblioum
Nikolay Shirokov
Published in Proceedings of the London Mathematical Society
Volume 109
Issue 5
Pages 1281-1303
ISSN 0024-6115
Publication year 2014
Published at Department of Mathematical Sciences, Mathematics
Pages 1281-1303
Language en
Links dx.doi.org/10.1112/plms/pdu038
Keywords Toeplitz operators d-bar equaion
Subject categories Mathematical Analysis

Abstract

We consider the ∂¯-equation in C1 in classes of functions with Gaussian decay at infinity. We prove that if the right-hand side of the equation is majorated by exp(−q|z|2), with some positive q, together with derivatives up to some order, and is orthogonal, as a distribution, to all analytical polynomials, then there exists a solution with decays, together with derivatives, as exp(−q′|z|2), for any q′

Page Manager: Webmaster|Last update: 9/11/2012
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