Kuelbs-Steadman spaces on Separable Banach spaces

2020/02/21 by Kalita, Hemanta, Hazarika, Bipan, Myers, Timothy
#26A39 #46B03 #46B20 #46B25 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2002.11512

Abstract

The purpose of this paper is to construct a new class of separable Banach spaces \K^p[\mathbbB], 1≤ p ≤ ∞. Each of these spaces contain the \mcL^p[\mathbbB] spaces, as well as the space \mfM[\R^\iy], of finitely additive measures as dense continuous compact embeddings. These spaces are of interest because they also contain the Henstock-Kurzweil integrable functions on \mathbbB. Finally, we offer a interesting approach to the Fourier transform on \K^p[\mathbbB].

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