Toeplitz Operators on m-harmonic Hardy Space Hpm(s) with 0 p = 1

Miroljub Jevtić

Publications de l'Institut Mathématique, _N_S_62 (1997) no. 76, p. 76 .

Résumé

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 $0

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Classification : 47G10 47B35