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

TL;DR

This paper characterizes q-uniformly convex and smooth Banach spaces using Carleson measures linked to Bessel operators, connecting geometric properties of Banach spaces with harmonic analysis tools.

Contribution

It introduces new characterizations of Banach space convexity and smoothness via Carleson measures and Poisson integrals associated with Bessel operators.

Findings

Characterizations of Banach spaces using Carleson measures.

Description of q-uniform convexity and smoothness through Poisson semigroup mappings.

Connection between geometric Banach space properties and harmonic analysis techniques.

Abstract

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.