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Toeplitz operators with singular symbols in polyanalytic Bergman spaces on the half-plane (1907.06878v2)
Published 16 Jul 2019 in math.FA and math.CV
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