Riesz transforms for Dirichlet spaces tamed by distributional curvature lower bounds

Syota Esaki; Zi Jian Xu; Kazuhiro Kuwae

Riesz transforms for Dirichlet spaces tamed by distributional curvature lower bounds

Probability 2023-08-25 v1

Authors: Syota Esaki , Zi Jian Xu , Kazuhiro Kuwae

Abstract

The notion of tamed Dirichlet space was proposed by Erbar, Rigoni, Sturm and Tamanini as a Dirichlet space having a weak form of Bakry-\'Emery curvature lower bounds in distribution sense. After their work, Braun established a vector calculus for it, in particular, the space of $L^2$ -normed $L^{\infty}$ -module describing vector fields, $1$ -forms, Hessian in $L^2$ -sense. In this framework, we establish the Littlewood-Paley-Stein inequality for $1$ -forms as an element of $L^p$ -cotangent bundles and boundedness of Riesz transforms, which partially solves the problem raised by Kawabi-Miyokawa.

Keywords

dirichlet space riesz transform distributional curvature lower bound littlewood-paley-stein inequality vector calculus bakry-emery

Cite

@article{arxiv.2308.12728,
  title  = {Riesz transforms for Dirichlet spaces tamed by distributional curvature lower bounds},
  author = {Syota Esaki and Zi Jian Xu and Kazuhiro Kuwae},
  journal= {arXiv preprint arXiv:2308.12728},
  year   = {2023}
}

Comments

68 pages. arXiv admin note: text overlap with arXiv:2307.12514; text overlap with arXiv:2108.12374 by other authors

Riesz transforms for Dirichlet spaces tamed by distributional curvature lower bounds

Abstract

Keywords

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