标题： 度量测度空间上的非绝对可积函数空间 显示英文标题

标题： Non-absolute integrable function spaces on metric measure spaces

摘要： Kuelbs-Steadman空间在本文中被引入到一个具有有限直径和有限正Borel测度的可分度量空间上。 也讨论了Lipschitz型的Kuelbs-Steadman空间。 还讨论了各种包含性质。 随后，我们在度量测度空间上引入HK-Sobolev空间，该空间在欧几里得情况下与HK-Sobolev空间一致。 在应用中，我们讨论了Hardy-Littlewood极大算子在度量测度空间上的Kuelbs-Steadman空间和HK-Sobolev空间上的有界性。 显示英文摘要

摘要： 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.