Approximation in weighted holomorphic Besov spaces in Cⁿ

2023/04/02 by Ali Abkar, Abkar, Ali
Mathematics · #Holomorphic and Operator Theory #Advanced Harmonic Analysis Research #Algebraic and Geometric Analysis

paper · pdf · doi:10.48550/arxiv.2304.00448

Abstract

We study certain weighted Bergman and weighted Besov spaces of holomorphic functions in the polydisk and in the unit ball. We seek Mergelyan-type conditions on the non-radial weight function to guarantee that the dilations of a given function tend to the same function in norm; in particular, we seek conditions on the non-radial weights to ensure that the analytic polynomials are dense in the space.

Related

• Carleson measures for weighted holomorphic Besov spaces in \Cⁿ
• Polyanalytic Besov spaces and approximation by dilatations
• Bounded operators on weighted spaces of holomorphic functions on the polydisk
• Non-radial weights and polynomial approximation in spaces of analytic functions
• Weighted Estimates for Operators Associated to the Bergman-Besov Kernels