2017/05/15 by Jun Liu, Dachun Yang, Liu, Jun +3
Mathematics · #42B25 #42B30 #46B70 #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Primary 42B35 #Secondary 46E30
paper · pdf · doi:10.48550/arxiv.1705.05188
openalex publication_date 2017/05/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let p(⋅): \mathbb Rn→(0,∞) be a variable exponent function satisfying the globally log-Hölder continuous condition, q∈(0,∞] and A be a general expansive matrix on ℝn. In this article, the authors first introduce the anisotropic variable Hardy-Lorentz space HAp(⋅),q(\mathbb Rn) 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 HAp(⋅),q(\mathbb Rn), respectively, in terms of the atom and the Lusin area function. As an application, the authors prove that the anisotropic variable Hardy-Lorentz space HAp(⋅),q(\mathbb Rn) severs as the intermediate space between the anisotropic variable Hardy space HAp(⋅)(\mathbb Rn) and the space L^∞(\mathbb Rn) via the real interpolation. This, together with a special case of the real interpolation theorem of H. Kempka and J. Vybíral on the variable Lorentz space, further implies the coincidence between HAp(⋅),q(\mathbb Rn) and the variable Lorentz space Lp(⋅),q(\mathbb Rn) when \mathopessinfx∈ℝnp(x)∈ (1,∞).