Toeplitz operators on hardy spaceH p (S) with 0<p?1

Abstract

LetB n be the unit ball inC n ,S is the boundary ofB n . We letL p (S) denote the usual Lebesgue spaces overS with respect to the normalized surface measure,H p (B n ) is its usua holomorphic subspace.H p (S) denotes the atomic Hardy spaces defined in [GL]. LetP∶L2(S)→H2(B n ) denote the orthogonal projection. For eachfeL∞(S), we useM f ∶L p (S)→L p (S) to denote the multiplication operator, and we define the Toeplitz operatorT f =PM f . The paper gives a characterization theorem onf such that the Toeplitz operatorsT f and\(T_{\bar f} \) are bounded fromH p (S)→H p (B n ) with 0<p≤1. Also several equivalent conditions are given.