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# Title: Vector-valued Littewood-Paley-Stein theory for semigroups II

Authors: Quanhua Xu
Abstract: Inspired by a recent work of Hyt\"onen and Naor, we solve a problem left open in our previous work joint with Mart\'{\i}nez 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 positive symmetric Markovian operator $T$ on a measure space $(\Omega, \mu)$. Moreover, we show that $T\otimes{\rm Id}_X$ extends to an analytic contraction on $L_p(\Omega; X)$ for any $1<p<\infty$ and any uniformly convex Banach space.
 Subjects: Functional Analysis (math.FA); Classical Analysis and ODEs (math.CA); Operator Algebras (math.OA) MSC classes: Primary: 46B20, 42B25. Secondary: 47B06, 47A35 Cite as: arXiv:1803.05107 [math.FA] (or arXiv:1803.05107v1 [math.FA] for this version)

## Submission history

From: Quanhua Xu [view email]
[v1] Wed, 14 Mar 2018 02:29:28 GMT (19kb)