A Derivative-Hilbert operator Acting on Dirichlet spaces

2022/07/18 by Xu, Yun, Ye, Shanli, Zhou, Zhihui · 1 citation
#30H99 #47B35 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2207.08368

Abstract

Let μ be a positive Borel measure on the interval [0,1). The Hankel matrix H_μ=(μ_n,k)_{n,k≥ 0} with entries μ_n,k=μ_n+k, where μ_n=∫_[0,1)tⁿdμ(t), induces formally the operator as DH_μ(f)(z)=∑_n=0^∞(∑_k=0^∞ μ_n,ka_k)(n+1)zⁿ , z∈ \mathbbD, where f(z)=∑_n=0^∞a_nzⁿ is an analytic function in \mathbbD. In this paper, we characterize those positive Borel measures on [0, 1) for which DH_μ is bounded (resp. compact) from Dirichlet spaces D_α( 0<α≤2 ) into D_β( 2≤β<4 ).

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