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

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 $(\Omega ,\mu )$. Moreover, we show that $T\otimes {\mathrm{Id}}_X$ extends to an analytic contraction on $L_p(\Omega ;X)$ for any $1<p<\infty$ and any uniformly convex Banach space $X$.

Cited by in corpus (3)

• Jump inequalities via real interpolation
• On analyticity of semigroups on Bochner spaces and on vector-valued noncommutative ${\mathrm{L}}^p$-spaces
• Vector-valued local approximation spaces