A Schur test for weighted mixed-norm spaces

Summary We prove a Schur test for mixed-norm spaces L^p,q, 1 < p,q < ∞. Also we prove another version of the Schur test for discrete weighted mixed-norm spaces l^p,q _w, 1 < p,q < ∞, and wis a weight. We show that if w ₁, and w ₂are two weight functions on the index sets Jx Iand K x Lrespectively, and A =(a _{ji, kl} ) _{j∈J, i∈I, k∈K, l∈L} is an infinite matrix, then under certain conditions, Ais a bounded operator from l^p,q _w1, 1 < p,q < ∞ to l^p,q _w2. This will be a key result in proving boundedness of important operators in our work in time-frequency analysis.