Anisotropic Variable Hardy-Lorentz Spaces and Their Real Interpolation
By Jun Liu, Dachun Yang, Wen Yuan. 2017
56 citations recorded by the source corpus.
Let $p(\cdot):\ \mathbb R^n\to(0,\infty)$ be a variable exponent function satisfying the globally log-Holder continuous condition, $q\in(0,\infty]$ and $A$ be a general expansive matrix on $\mathbb{R}^n$. In this article, the authors first introduce the anisotropic variable Hardy-Lorentz space $H_A^{p(\cdot),q}(\mathbb R^n)$ associated with $A$, via the radial grand maximal function, and then establish its radial or non-tangential maximal function characterizations. Moreover, the authors also obtain characterizations of $H_A^{p(\cdot),q}(\mathbb R^n)$, respectively, in terms of the atom and the Lusin area function. As an application, the authors prove that the anisotropic variable Hardy-Lorentz space $H_A^{p(\cdot),q}(\mathbb R^n)$ severs as the intermediate space between the anisotropic variable Hardy space $H_A^{p(\cdot)}(\mathbb R^n)$ and the space $L^\infty(\mathbb R^n)$ via the real interpolation. This, together with a special case of the real interpolation theorem of H. Kempka and J. Vybiral on the variable Lorentz space, further implies the coincidence between $H_A^{p(\cdot),q}(\mathbb R^n)$ and the variable Lorentz space $L^{p(\cdot),q}(\mathbb R^n)$ when $\mathop\mathrm{essinf}_{x\in\mathbb{R}^n}p(x)\in (1,\infty)$.
Subfields: Applied Mathematics
View Paper: https://www.semanticscholar.org/paper/b9402758354f16717c6e27359e260223263b247b
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
Citations in the corpus
- Atomic and Littlewood–Paley Characterizations of Anisotropic Mixed-Norm Hardy Spaces and Their Applications (2018, methodology): “For more progresses about the theory of anisotropic function spaces on R, we refer the reader to [11, 25, 45, 48, 49, 51, 53, 54, 55] for anisotropic Hardy-type spaces and to [7, 8, 9, 46, 47, 56] for anisotropic Besov and TriebelLizorkin spaces.”
- Real-variable characterizations of Orlicz-slice Hardy spaces (2018, background): “In recent decades, in order to meet the requirements arising in the study of the boundedness of operators, partial differential equations and some other fields, various variants of Hardy spaces have been introduced and developed, such as weak Hardy spaces (see, for example, [17, 20]), Hardy-Lorentz ”
- Variable Hardy–Lorentz spaces Hp(·),q(Rn) (2018, background): “[41] investigated the variable anisotropic Hardy space H p(⋅) A (Rn) associated with some expansive matrix A, via the non-tangential grand maximal function, which is a generalization of the classical isotropic variable Hardy space of Nakai and Sawano [44] as well as of Cruz-Uribe and Wang [18].”