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<p>We study certain weighted Bergman and weighted Besov spaces of holomorphic functions in the polydisk and in the unit ball. We seek conditions on the weight functions to guarantee that the dilations of a given function converge to the same function in norm; in particular, we seek conditions on the weights to ensure that the analytic polynomials are dense in the space.</p>

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Approximation in weighted holomorphic Besov spaces on polydisk and unit ball

  • 期刊论文

  • 发表日期：

    2025年8月4日

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  • Ali Abkar

摘要

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