Kuelbs-Steadman spaces for Banach space-valued measures

Abstract

We introduce Kuelbs-Steadman-type spaces for real-valued functions, with respect to countably additive measures, taking values in Banach spaces. We investigate their main properties and embeddings in $L^p$-type spaces, considering both the norm associated to norm convergence of the involved integrals and that related to weak convergence of the integrals.

arXiv comment12 pages

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Cited by in corpus (1)

• HK-Sobolev space $W{S}^{k,p}$ on ${\mathbb{R}}^{\infty }$ and Bessel Potential