Compactness in Lipschitz spaces and around
Volume 272 / 2023
Studia Mathematica 272 (2023), 81-112
MSC: Primary 46B50; Secondary 26A16, 46E15, 46E99.
DOI: 10.4064/sm221020-16-3
Published online: 6 September 2023
Abstract
The aim of the paper is to characterize (pre)compactness in the spaces of Lipschitz/Hölder continuous mappings from an arbitrary (not necessarily compact) metric space to a normed space. To this end some extensions and generalizations of existing compactness criteria for the spaces of bounded and continuous mappings with values in normed spaces are established. Those auxiliary results, which are interesting in their own right since they use a new concept of equicontinuity, are based on an abstract compactness criterion related to the recently introduced notion of an equinormed set.
