Hardy-Littlewood maximal operator on variable Lebesgue spaces with respect to a probability measure. Issue 3 (4th March 2022)

• Record Type: Journal Article
• Authors: Moreno, Jorge; Pineda, Ebner; Rodriguez, Luz; Urbina, Wilfredo O.
• Is Part Of: Quaestiones mathematicae. Volume 45:Issue 3(2022)
• Page Start: 385
• Page End: 407
• Publication Date: 2022-03-04
• Subjects: Primary: 42B25 -- 42B35 -- Secondary: 46E30 -- 47G10; Harmonic analysis -- Radon measure -- Hardy-Littlewood maximal functions -- variable Lebesgue spaces; Mathematics -- Periodicals; 510.5
• DOI: 10.2989/16073606.2021.1882603
• Languages: English
• ISSNs: 1607-3606

Abstract

Abstract: In this paper we are going to prove that the Hardy-Litllewood maximal operators on variable Lebesgue spaces L p(·) ( µ ) with respect to a probability Borel measure µ, are weak type and strong type for two conditions of regularity on the exponent function p (·); following [2] and [3]. Also following [2] we extend some important properties of this operator to a probability Borel measure µ, the key to extend these results is using the Besicovitch covering lemma instead of the Calderón-Zygmund decomposition.