Generalized Cesàro-like operator from a class of analytic function spaces to analytic Besov spaces

2023/09/06 by Tang, Pengcheng
#Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2309.02717

Abstract

Let μ be a finite positive Borel measure on [0,1) and f(z)=∑_n=0^∞a_nzⁿ ∈ H(\mathbbD). For 0<α<∞, the generalized Cesàro-like operator C_μ,α is defined by \mathcal C_μ,α(f)(z)=∑^∞_n=0(μ_n∑ⁿ_k=0(Γ(n-k+α))/(Γ(α)(n-k)!)a_k)zⁿ, z∈ \mathbbD, where, for n≥ 0, μ_n denotes the n-th moment of the measure μ, that is, μ_n=∫₀¹ tⁿdμ(t). For s>1, let X be a Banach subspace of H(\mathbbD) with Λ^s_(1)/(s)⊂ X⊂\mathcal B. In this paper, for 1≤ p <∞, we characterize the measure μ for which C_μ,α is bounded(or compact) from X into analytic Besov space B_p.

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