Smoothing of uniformly continuous mappings in \(L_ p\) spaces
The paper deals with approximation of uniformly continuous mappings of the unit ball \(B_ p\subset L_ p\) into \(L_ q\) by functions from Hölder classes. For spaces defined on a measure space with a \(\sigma\)- additive measure, lower bounds for the Hölder exponent are established and a quantitative dependence on further geometric properties is studied (general Banach spaces, uniformly convex spaces, superreflexive spaces). The Hölder exponents are shown to be the best for \(L_ p\) spaces on the real line.
approximation of uniformly continuous mappings
scientific article; zbMATH DE number 687511