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/

Zendy Plus

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

Zendy Tools

Zendy Open

Let $\mathcal{X}$ be a metric space with doubling measure and $L$ anon-negative self-adjoint operator on $L^2(\mathcal{X})$ whose heat kernelssatisfy the Gaussian upper bound estimates. Assume that the growth function$\varphi:\ \mathcal{X}\times[0,\infty) \to[0,\infty)$ satisfies that$\varphi(x,\cdot)$ is an Orlicz function and $\varphi(\cdot,t)\in {\mathbbA}_{\infty}(\mathcal{X})$ (the class of uniformly Muckenhoupt weights). Let$H_{\varphi,\,L}(\mathcal{X})$ be the Musielak-Orlicz-Hardy space defined viathe Lusin area function associated with the heat semigroup of $L$. In thisarticle, the authors characterize the space $H_{\varphi,\,L}(\mathcal{X})$ bymeans of atoms, non-tangential and radial maximal functions associated with$L$. In particular, when $\mu(\mathcal{X})<\infty$, the local non-tangentialand radial maximal function characterizations of $H_{\varphi,\,L}(\mathcal{X})$are obtained. As applications, the authors obtain various maximal function andthe atomic characterizations of the "geometric" Musielak-Orlicz-Hardy spaces$H_{\varphi,\,r}(\Omega)$ and $H_{\varphi,\,z}(\Omega)$ on the stronglyLipschitz domain $\Omega$ in $\mathbb{R}^n$ associated with second-orderself-adjoint elliptic operators with the Dirichlet and the Neumann boundaryconditions; even when $\varphi(x,t):=t$ for any $x\in\mathbb{R}^n$ and$t\in[0,\infty)$, the equivalent characterizations of $H_{\varphi,\,z}(\Omega)$given in this article improve the known results via removing the assumptionthat $\Omega$ is unbounded.

Atomic and Maximal Function Characterizations of Musielak-Orlicz-Hardy  Spaces Associated to Non-negative Self-adjoint Operators on Spaces of  Homogeneous Type