Smoothing of uniformly continuous mappings in Lp spaces
Copyright policy )Smoothing of uniformly continuous mappings in Lp 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.
- Lomonosov Moscow State University Russian Federation
superreflexive spaces, Hölder continuity, uniformly convex spaces, approximation of uniformly continuous mappings, Rate of convergence, degree of approximation, Hölder exponent, Approximation by other special function classes, Hölder classes, Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
superreflexive spaces, Hölder continuity, uniformly convex spaces, approximation of uniformly continuous mappings, Rate of convergence, degree of approximation, Hölder exponent, Approximation by other special function classes, Hölder classes, Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
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