Carleson Measures and Toeplitz Type Operators on Hardy Type Tent Spaces

Abstract

In this paper, we obtain some characterizations on Carleson measures for Hardy type tent spaces on the unit ball through products of functions. As applications, we characterize the boundedness and compactness of Toeplitz type operators between distinct Hardy type tent spaces in terms of Carleson measures. Moreover, we obtain bounded and compact Toeplitz type operators $$T_{\mu }^{\beta }$$ from weighted Bergman spaces $$A_{n+\alpha }^p$$ to Hardy spaces $$H^q$$ , and describe the membership in the Schatten classes $$S_p(A_{n+\alpha }^2,H^2)$$ of Toeplitz type operators $$T_{\mu }^{\beta }$$ for $$0<p<\infty $$ .