Non-absolute integrable function spaces on metric measure spaces

2023/10/31 by Hazarika, Parthapratim Saha Bipan, Kalita, Hemanta
#46B25 #46E35 #46E36 #46F25 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2311.05637

Abstract

Kuelbs-Steadman spaces are introduced in this article on a separable metric space with finite diameter and finite positive Borel measure. Kuelbs-Steadman spaces of the Lipschitz type are also discussed. Various inclusion properties are also discussed. In the sequel, we introduce HK-Sobolev spaces on metric mesure space which coincides with HK-Sobolev space in the Euclidean case. In application, we discuss the boundedness of Hardy-Littlewood maximal operator on Kuelbs-Steadman spaces and HK-Sobolev spaces over a metric measure space.

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