Toeplitz operators on $M$-harmonic Hardy space $H^p_m(S)$ with $0

Miroljub Jevti\'c

Matematicki fakultet, Beograd, Yugoslavia

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Abstract: Let $B^n$ be the unit ball in $C^n$, $S$ is the boundary of $B^n$. Let $L^p(S)$ denote the usual Lebesgue spaces over $S$ with respect to the normalized surface measure, $H^p_m (B^n)$ is the Hardy space of $M$-harmonic functions and $H^p_{at} (S)$ denotes the atomic Hardy spaces defined in [4]. Let $P: L^2 (S)\to H^2_m (B^n)$ denote the Poisson--Szëgo projection. We use $M_f :L^p(S)\to L^p(S)$ to denote the multiplication operator, and we define the Toeplitz operator $T_f = PM_f$. The paper gives characterization theorems on $f$ such that the Toeplitz operator $T_f$ is bounded from $H^p_{at} (S)\to H^p_m (B^n)$ with $0Classification (MSC2000): 47G10; 47B35

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Electronic fulltext finalized on: 1 Nov 2001. This page was last modified: 16 Nov 2001.

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