Maximal and Calderón–Zygmund operators on the local variable Morrey–Lorentz spaces and some applications

Abstract

In this paper, we give the definition of local variable Morrey–Lorentz spaces (Formula presented.) which are a new class of functions. Also, we prove the boundedness of the Hardy–Littlewood maximal operator M and Calderón–Zygmund operators T on these spaces. Finally, we apply these results to the Bochner–Riesz operator (Formula presented.), identity approximation (Formula presented.) and the Marcinkiewicz operator (Formula presented.) on the spaces (Formula presented.). © 2021 Informa UK Limited, trading as Taylor & Francis Group.