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Article Dans Une Revue International Mathematics Research Notices Année : 2020

Vector-valued Littlewood-Paley-Stein Theory for Semigroups II

Résumé

Abstract Inspired by a recent work of Hytönen and Naor, we solve a problem left open in our previous work joint with Martínez 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 diffusion Markovian operator on a measure space $(\Omega , \mu )$. Moreover, we show that $T\otimes{ \textrm{Id}}_X$ extends to an analytic contraction on $L_p(\Omega ; X)$ for any $1<p<\infty $ and any uniformly convex Banach space $X$.
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Dates et versions

hal-03541797 , version 1 (24-01-2022)

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Quanhua Xu. Vector-valued Littlewood-Paley-Stein Theory for Semigroups II. International Mathematics Research Notices, 2020, 2020 (21), pp.7769-7791. ⟨10.1093/imrn/rny200⟩. ⟨hal-03541797⟩
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