Upper bounds for the exponent of Holder mappings in problems of approximation and extension

摘要

Under some suitable assumptions on Banach spaces X and Y, we give upper bounds for the exponent alpha(B-X, Y) so that uniformly continuous functions from the closed unit ball BX of X to Y can be uniformly approximated by beta-Holder functions for beta < alpha(B-X, Y). For Banach lattices X with some lower p < 8 estimate, our bound gives the exact value of the critical exponent alpha(B-X, l(q)), which was known for X = l(p). We notice that such estimates give upper bounds in the setting of isomorphic extension of Holder maps.