Maximal function characterizations of variable Hardy spaces associated with non-negative self-adjoint operators satisfying Gaussian estimates

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• 作者：Ciqiang Zhuo ^{cqzhuo@mail.bnu.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Dachun Yang ; ^{dcyang@bnu.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 42B25 ; secondary ; 42B30 ; 42B35 ; 35K08
• 刊名：Nonlinear Analysis
• 出版年：2016
• 出版时间：August 2016
• 年：2016
• 卷：141
• 期：Complete
• 页码：16-42
• 全文大小：747 K

文摘

Let $p(\cdot ):{\mathbb{R}}^n\to (0,1]$ be a variable exponent function satisfying the globally log$log$-Hölder continuous condition and L$L$ a non-negative self-adjoint operator on L²(Rⁿ)$L^2\left({\mathbb{R}}^n\right)$ whose heat kernels satisfying the Gaussian upper bound estimates. Let 421145cc8602f71f1aaa935611d">$H_L^{p(\cdot )}\left({\mathbb{R}}^n\right)$ be the variable exponent Hardy space defined via the Lusin area function associated with the heat kernels {e^−t2L}_t∈(0,∞)${\left\{e^{-t^{2}L}\right\}}_{t\in (0,\infty )}$. In this article, the authors first establish the atomic characterization of 421145cc8602f71f1aaa935611d">$H_L^{p(\cdot )}\left({\mathbb{R}}^n\right)$; using this, the authors then obtain its non-tangential maximal function characterization which, when p(⋅)$p(\cdot )$ is a constant in (0,1]$(0,1]$, coincides with a recent result by L. Song and L. Yan (2016) and further induces the radial maximal function characterization of 421145cc8602f71f1aaa935611d">$H_L^{p(\cdot )}\left({\mathbb{R}}^n\right)$ under an additional assumption that the heat kernels of L$L$ have the Hölder regularity.