Vector-valued Littewood-Paley-Stein theory for semigroups II

2018/03/14 by Xu, Quanhua
#42B25. Secondary: 47B06 #47A35 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #Primary: 46B20

paper · doi:10.48550/arxiv.1803.05107

Abstract

Inspired by a recent work of Hytönen and Naor, we solve a problem left open in our previous work joint with Mart'ınez and Torrea on the vector-valued Littlewood-Paley-Stein theory for symmetric diffusion semigroups. We prove a similar result in the discrete case, namely, for any T which is the square of a symmetric Markovian operator on a measure space (Ω, μ). Moreover, we show that T⊗\rm Id_X extends to an analytic contraction on L_p(Ω; X) for any 1

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