Sublinear operators on mixed-norm Hardy spaces with variable exponents

Abstract

In this paper, we define and study the mixed-norm Hardy spaces with variable exponents. We establish some general principles for the mapping properties of sublinear operators on the mixed-norm Hardy spaces with variable exponents. By using these principles, we obtain the mapping properties of the Calderón–Zygmund operators, the oscillatory singular integral operators, the multiplier operators, the Littlewood–Paley functions, the intrinsic square functions, the parametric Marcinkiewicz integrals and the maximal Bochner–Riesz means on the mixed-norm Hardy spaces with variable exponents.