English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper, we introduce the notion of $L^p$-Green-tight measures of$L^p$-Kato class in the framework of symmetric Markov processes. The class of$L^p$-Green-tight measures of $L^p$-Kato class is defined by the $p$-th powerof resolvent kernels. We first prove that under the $L^p$-Green tightness ofthe measure $\mu$, the embedding of extended Dirichlet space into$L^{2p}(E;\mu)$ is compact under the absolute continuity condition fortransient Markov processes, which is an extension of recent seminal work byTakeda. Secondly, we prove the coincidence between two classes of$L^p$-Green-tightness, one is originally introduced by Zhao, and another one isinvented by Chen. Finally, we prove that our class of $L^p$-Green-tightmeasures of $L^p$-Kato class coincides with the class of $L^p$-Green tightmeasures of Kato class in terms of Green kernel under the global heat kernelestimates. We apply our results to $d$-dimensional Brownian motionandrotationally symmetric relativistic $\alpha$-stable processes on$\mathbb{R}^d$.

$L^p$-Green-tight measures of $L^p$-Kato class for symmetric Markov processes