Calderón–Zygmund operators, Bochner–Riesz means, and parametric Marcinkiewicz integrals on Hardy–Morrey spaces with variable exponents

Abstract

We obtain the boundedness of Calderón–Zygmund operators on the entire Hardy–Morrey spaces with variable exponents. We obtain this result by refining the extrapolation theory. This refined extrapolation theory also gives the boundedness of Fourier multipliers, Bochner–Riesz means, and parametric Marcinkiewicz integrals on Hardy–Morrey spaces with variable exponents.