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

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:482

Article

Betancor, Jorge J.¹  Farina, Juan C.¹  Galli, Vanesa²  Molina, Sandra M.² 

[1] Univ La Laguna, Dept Anal Matemat, Campus Anchieta,Avda Astrofis Sanchez S-N, San Cristobal la Laguna 38721, Ste Cruz De Ten, Spain

[2] Univ Nacl Mar Del Plata, Fac Ciencias Exactas & Nat, Dept Matemat, Funes 3350, RA-7600 Mar Del Plata, Buenos Aires, Argentina

关键词: Uniformly convex;    Uniformly smooth;    Littlewood-Paley;    Area integrals;   

DOI  :  10.1016/j.jmaa.2019.123534

来源: Elsevier

【 摘 要 】

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. (C) 2019 Published by Elsevier Inc.

【 授权许可】

Free