We prove a Schur test for mixed-norm spaces Lp,q, 1 < p,q < ∞. Also we prove another version of the Schur test for discrete weighted mixed-norm spaces lp,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 lp,q w1, 1 < p,q < ∞ to lp,q w2. This will be a key result in proving boundedness of important operators in our work in time-frequency analysis.
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