Characterization of uniformly convex and smooth Banach spaces by using Carleson measures in Bessel settings

Details Characterization of uniformly convex and smooth Banach spaces by using Carleson measures in Bessel settings Characterization of uniformly convex and smooth Banach spaces by using Carleson measures in Bessel settings

2011-07-28

arxiv.org/abs/1107.5698v1

Mathematics

Classical Analysis and ODEs

32 pages

Scientific paper

In this paper we obtain new characterizations of the q-uniformly convex and smooth Banach spaces by using Carleson measures. These measures are defined by Poisson integral associated with Bessel operators and Banach valued BMO-functions. By the way we describe q-uniformly convexity and smoothness of a Banach space in terms of the mapping properties of the Lusin integral defined by the Poisson semigroup for Bessel operators.

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