English

Toeplitz operators with singular symbols in polyanalytic Bergman spaces on the half-plane

Functional Analysis 2019-12-12 v2 Complex Variables

Abstract

Using the approach based on sesquilinear forms, we introduce Toeplitz operator in the analytic Bergman space on the upper half-plane with strongly singular symbols, derivatives of measures. Conditions for boundedness and compactness of such operators are found. A procedure of reduction of Toeplitz operators in Bergman spaces of polyanalytic functions to operators with singular symbols in the analytic Bergman space by means of the creation-annihilation structure is elaborated, which leads to the description of the properties of the former operators

Keywords

Cite

@article{arxiv.1907.06878,
  title  = {Toeplitz operators with singular symbols in polyanalytic Bergman spaces on the half-plane},
  author = {Grigori Rozenblum and Nikolai Vasilevski},
  journal= {arXiv preprint arXiv:1907.06878},
  year   = {2019}
}