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We study the class of (p, q)-regular operators between quasi-Banach lattices. In particular, a representation of this class as the dual of a certain tensor norm for Banach lattices is given. We also provide some factorization results for (p, q)-regular operators yielding new Marcinkiewicz–Zygmund type inequalities for Banach function spaces. An extension theorem for \((q, \infty )\)-regular operators defined on a subspace of \(L_q\) is also given.

(p, q)-Regular operators between Banach lattices