Toeplitz Operators with Radial Symbols on Weighted Pluriharmonic Bergman Spaces over Reinhardt Domains - Zhi-Ling Sun; Feng Qi; Wei-Shih Du (Axioms, 2025)
In this paper, we design an operator A restricted to a weighted pluriharmonic Bergman space <semantics><msubsup>bμ2</msubsup>(Ω)</semantics> over the Reinhardt domains, with an isometric isomorphism between <semantics><msubsup>bμ2</msubsup>(Ω)</semantics> and the subset of <semantics>l2(Zn)</semantics>. Furthermore, we show that Toeplitz operators <semantics>Ta</semantics> with radial symbols are unitary to the multiplication operators <semantics>γaI</semantics> on sequence space <semantics>l2</semantics> by using the operator A. The Wick function of a Toeplitz operator with a radial symbol provides some features to the operator, establishing its spectral decomposition. Finally, we specify the obtained results on the Reinhardt domains for the unit ball.