A DERIVATIVE-HILBERT OPERATOR ACTING ON HARDY SPACES  

作　　者：叶善力 冯光豪 Shanli YE;Guanghao FENG(School of Science,Zhejiang University of Science and Technology,Hangzhou 310023,China)

机构地区：[1]School of Science,Zhejiang University of Science and Technology,Hangzhou 310023,China

出　　处：《Acta Mathematica Scientia》2023年第6期2398-2412,共15页数学物理学报（B辑英文版）

基　　金：supported by the Zhejiang Provincial Natural Science Foundation (LY23A010003);the National Natural Science Foundation of China (11671357).

摘　　要：Letμbe a positive Borel measure on the interval[0,1).The Hankel matrixHμ=(μn,k)n,k≥0 with entries μn,k=μn+k,whereμn=∫[0,1)tndμ(t),induces formally the operator asDHμ(f)(z)=∞∑n=0(∞∑k=0 μn,kak)z^(n),z∈D,where f(z)=∞∑n=0a_(n)z^(n) is an analytic function in D.We characterize the positive Borel measures on[0,1)such thatDHμ(f)(z)=f[0,1)f(t)/(1-tz)^(2)dμ(t) for all f in the Hardy spaces Hp(0<p<∞),and among these we describe those for which is a bounded(resp.,compact)operator from Hp(0<p<∞)into Hq(q>p and q≥1).We also study the analogous problem in the Hardy spaces H^(p)(1≤p≤2).

关 键 词：Derivative-Hilbert operators Hardy spaces Carleson measures 

分 类 号：O177[理学—数学]