The Ces`aro-like operator on some analytic function spaces

2023/05/05 by Pengcheng Tang, Tang, Pengcheng · 1 citation
Mathematics · #Advanced Harmonic Analysis Research #Holomorphic and Operator Theory #Advanced Banach Space Theory

paper · pdf · doi:10.48550/arxiv.2305.03333

Abstract

Let μ be a finite positive Borel measure on the interval [0, 1) and f(z)=∑_n=0^∞a_nzⁿ ∈ H(\mathbbD). The Cesàro-like operator is defined by \mathcal C_μ (f)(z)=∑^∞_n=0(μ_n∑ⁿ_k=0a_k)zⁿ, z∈ \mathbbD, where, for n≥ 0, μ_n denotes the n-th moment of the measure μ, that is, μ_n=∫_{[0, 1)} tⁿdμ(t). Let X and Y be subspaces of H( \mathbbD), the purpose of this paper is to study the action of \mathcal C_μ on distinct pairs (X, Y). The spaces considered in this paper are Hardy space H^p(0

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