Characterizing compact sets in L^p-spaces and its application

2022/05/13 by Koshino, Katsuhisa
#46E30 #57N20 #FOS: Mathematics #Functional Analysis (math.FA) #General Topology (math.GN) #Primary 54C35 #Secondary 46B50

paper · doi:10.48550/arxiv.2205.06864

Abstract

In this paper, we give a characterization of compact sets in L^p-spaces on metric measure spaces, which is a generalization of the Kolmogorov-Riesz theorem. Using the criterion, we investigate the topological type of the space consisting of lipschitz maps with bounded supports.

Related

• Kolmogorov\unicodex2013Riesz compactness in asymptotic L_p spaces
• Compactness in Lipschitz spaces and around
• The mapping of compact into the set of its Chebyshev centres is Lipschitz in the space lⁿ_∞
• Compactness in the Lebesgue-Bochner spaces L^p(μ;X)
• Spaceability of sets of p-compact maps