Atomic Decomposition and Carleson Measures for Weighted Mixed Norm Spaces

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(s), induced by a positive Borel measure mu, on the full range of parameters O < p,q,s < infinity.