论文标题
局部orlicz-slice hardy空间的可实现特征，并应用于双线性分解
Real-Variable Characterizations of Local Orlicz-Slice Hardy Spaces with Application to Bilinear Decompositions
论文作者
论文摘要
最近，两种双线性分解$ h^1（\ MATHBB {r}^n）\ times \ times \ mathrm {\，bmo}（\ Mathbb {r}^n）\ subset l^1（\ subset l^1（\ subset l^1） $ h^1（\ mathbb {r}^n）\ times \ times \ mathrm {bmo}（\ mathbb {r}^n）\ subset l^1（\ mathbb {r}^n） + h^{\ log}（\ log}（\ log}（\ mathbb {rmathbb {r}^n）$已建立。在本文中，作者在某种意义上证明了前者是锋利的，而后者则不是。为此，作者首先介绍本地的$ h_ \ ast^φ（\ mathbb {r}^n）$的局部orlicz-slice hardy空间，该局部orlicz arlicz hardy空间由A. bonami和J. Feuto引入的介绍，并作为特殊情况通过其表征，即使在符号中获得各种功能，并获得了各种功能，并可以通过各种功能，并获得了各种功能，并可以通过零件来建立Ats，并获得了各种功能，并可以通过零件来获得。 $ h_ \ ast^φ（\ mathbb r^n）$。关系$ h_ \ ast^φ（\ mathbb {r}^n）\ subsetneqq h^{\ log}（\ mathbb {r}^n）$也被澄清。
Recently, both the bilinear decompositions $h^1(\mathbb{R}^n)\times \mathrm{\,bmo}(\mathbb{R}^n) \subset L^1 (\mathbb{R}^n)+h_\ast^Φ(\mathbb{R}^n)$ and $h^1(\mathbb{R}^n) \times \mathrm{bmo}(\mathbb{R}^n) \subset L^1 (\mathbb{R}^n) + h^{\log}(\mathbb{R}^n)$ were established. In this article, the authors prove in some sense that the former is sharp, while the latter is not. To this end, the authors first introduce the local Orlicz-slice Hardy space which contains the variant $h_\ast^Φ(\mathbb{R}^n)$ of the local Orlicz Hardy space introduced by A. Bonami and J. Feuto as a special case, and obtain its dual space by establishing its characterizations via atoms, finite atoms and various maximal functions, which are new even for $h_\ast^Φ(\mathbb R^n)$. The relationships $h_\ast^Φ(\mathbb{R}^n) \subsetneqq h^{\log}(\mathbb{R}^n)$ is also clarified.
