Research Article

Maximal and singular operators in the local “complementary” generalized variable exponent Morrey spaces on unbounded sets

Published in: Quaestiones Mathematicae
Volume 43 , issue 10 : Entrepreneurship and Africa’s Cultural Context , 2024 , pages: 1487–1512
DOI: 10.2989/16073606.2019.1635539
Author(s): Canay Aykol , Turkey, Xayyam A. Badalov , Azerbaijan, Javanshir J. Hasanov , Azerbaijan,
Keywords: Maximal operator, singular integral operators, commutators, local “complementary” generalized Morrey space, BMO space, Maximal operator, singular integral operators, commutators, local “complementary” generalized Morrey space, BMO space,
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Abstract

In this paper we consider local “complementary” generalized Morrey spaces with variable exponent p(x) and a general function ω(r) defining a Morrey-type norm. We prove the boundedness of the Hardy-Littlewood maximal operator and Calderón-Zygmund singular operators with standard kernel in such spaces in case of unbounded sets Ω ⊂ ℝ n . Also we prove the boundedness of commutators of Hardy-Littlewood maximal operator and Calderón-Zygmund singular integral operators.
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