Calculus of Variations and Geometric Measure Theory

A. Carbonaro - L. Tamanini - D. Trevisan

Boundedness of Riesz transforms on $RCD(K,\infty)$ spaces

created by tamanini1 on 11 Sep 2023



Inserted: 11 sep 2023
Last Updated: 11 sep 2023

Year: 2023

ArXiv: 2308.16294 PDF


For $1<p<\infty$, we prove the $L^p$-boundedness of the Riesz transform operators on metric measure spaces with Riemannian Ricci curvature bounded from below, without any restriction on their dimension. This large class of spaces include e.g. that of Hilbert spaces endowed with a log-concave probability measure. As a consequence, we extend the range of the validity of the Lusin-type approximation of Sobolev by Lipschitz functions, previously obtained by L. Ambrosio, E. Bru\`e and the third author in the quadratic case, i.e. $p=2$. The proofs are analytic and rely on computations on an explicit Bellman function.