Uniformly convex and smooth Banach spaces and Lp-boundedness properties of Littlewood-Paley and area functions associated with semigroups

2019/04/11 by Jorge J. Betancor, Betancor, Jorge J., Juan C. Fariña +5
Mathematics · #43A15 #46B20 #47D03 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:43A15 #msc:46B20 #msc:47D03

paper · pdf · doi:10.48550/arxiv.1904.05641

arxiv created 2019/04/11 · arxiv updated 2019/04/12

Abstract

In this paper we obtain new characterizations of the uniformly convex and smooth Banach spaces. These characterizations are established by using Lp-boundedness properties of Littlewood-Paley functions and area integrals associated with heat semigroups and involving fractional derivatives. Our results apply for instance by considering the heat semigroups defined by Hermite and Laguerre operators that do not satisfy the Markovian property.

Related

• Area Littlewood-Paley functions associated with Hermite and Laguerre operators
• Littlewood-Paley-Stein theory and Banach spaces in the inverse Gaussian setting
• Vector-valued Littlewood-Paley-Stein theory for semigroups
• Fractional Vector-Valued Littlewood-Paley-Stein Theory for Semigroups
• Equivalence of Littlewood-Paley square function and area function characterizations of weighted product Hardy spaces associated to operators