A DERIVATIVE--HILBERT OPERATOR ACTING FROM BESOV SPACES INTO BLOCH SPACE.

Authors :: LIYUN ZHAO
ZHENYOU WANG
ZHIRONG SU
Source :: Journal of Mathematical Inequalities; Sep2022, Vol. 16 Issue 3, p1229-1242, 14p
Publication Year :: 2022
Abstract: If μ is a positive Borel measure on the interval [0, 1), we let 퓗<subscript>μ</subscript> be the Hankel matrix 퓗<subscript>μ</subscript> = ( μ<subscript>n,k</subscript>)<subscript>n,k≥0</subscript> with entries μ<subscript>n,k</subscript> = μ<subscript>n+k</subscript> and μ<subscript>n</subscript> = ∫<subscript>[0,1</subscript>) t<superscript>n</superscript>d μ(t). Using 퓗<subscript>μ</subscript>, Ye and Zhou first defined the Derivative-Hilbert operator as D퓗<subscript>μ</subscript>(f)(z) = ... (n+1)z<superscript>n</superscript>, z ∈ 픻, where f (z)= ... is an analytic function in 픻. In this paper, we characterize the measure μ for which D퓗<subscript>μ</subscript> is a bounded (resp., compact) operator from Besov space B<subscript>p</subscript> into Bloch space B with 1 < p < ∞. [ABSTRACT FROM AUTHOR]