Atomic decomposition and Carleson measures for weighted mixed norm spaces

Abstract

The purpose of this paper is to establish an atomic decomposition for functions in the weighted mixed norm space $A_{\omega }^{p,q}$ induced by a radial weight $\omega$ in the unit disc admitting a two-sided doubling condition. The obtained decomposition is further applied to characterize Carleson measures for $A_{\omega }^{p,q}$, and bounded differentiation operators $D^{(n)}(f)=f^{(n)}$ acting from $A_{\omega }^{p,q}$ to $L_{\mu }^p$, induced by a positive Borel measure $\mu$, on the full range of parameters $0<p,q,s<\infty$.