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Some weighted estimates for the ∂̅-equation and a finite rank theorem for Toeplitz operators in the Fock space
Journal article, 2014

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′

Toeplitz operators d-bar equaion

## Author

### Grigori Rozenblioum

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematics

### Nikolay Shirokov

National Research University Higher School of Economics

Saint Petersburg State University - Spsu

#### Proceedings of the London Mathematical Society

0024-6115 (ISSN) 1460-244X (eISSN)

Vol. 109 5 1281-1303### Roots

Basic sciences

### Subject Categories

Mathematical Analysis

### DOI

10.1112/plms/pdu038