Kuelbs–Steadman Spaces for Banach Space-Valued Measures

Antonio Boccuto, Bipan Hazarika and Hemanta Kalita
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Antonio Boccuto: Department of Mathematics and Computer Sciences, University of Perugia, via Vanvitelli, 1 I-06123 Perugia, Italy
Bipan Hazarika: Department of Mathematics, Gauhati University, Guwahati 781014, Assam, India
Hemanta Kalita: Department of Mathematics, Patkai Christian College (Autonomous), Dimapur, Patkai 797103, Nagaland, India

Mathematics, 2020, vol. 8, issue 6, 1-14

Abstract: We introduce Kuelbs–Steadman-type spaces ( K S p spaces) for real-valued functions, with respect to countably additive measures, taking values in Banach spaces. We investigate the main properties and embeddings of L q -type spaces into K S p spaces, considering both the norm associated with the norm convergence of the involved integrals and that related to the weak convergence of the integrals.

Keywords: Kuelbs–Steadman space; Henstock–Kurzweil integrable function; vector measure; dense embedding; completely continuous embedding; Köthe space; Banach lattice (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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