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arXiv · 2311.05637

Non-absolute integrable function spaces on metric measure spaces

Parthapratim Saha Bipan Hazarika·Hemanta Kalita
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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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Parthapratim Saha Bipan Hazarika, Hemanta Kalita. 2023-10-31. Non-absolute integrable function spaces on metric measure spaces. https://arxiv.org/abs/2311.05637

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