Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5774722 | Journal of Mathematical Analysis and Applications | 2017 | 38 Pages |
Abstract
Let p(â
):Rnâ(0,â] be a variable exponent function satisfying the globally log-Hölder continuous condition, qâ(0,â] and A be a general expansive matrix on Rn. In this article, the authors first introduce the anisotropic variable Hardy-Lorentz space HAp(â
),q(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(â
),q(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(â
),q(Rn) serves as the intermediate space between the anisotropic variable Hardy space HAp(â
)(Rn) and the space Lâ(Rn) via the real interpolation. This, together with a special case of the real interpolation theorem of H. Kempka and J. VybÃral on the variable Lorentz space, further implies the coincidence between HAp(â
),q(Rn) and the variable Lorentz space Lp(â
),q(Rn) when essinfxâRnp(x)â(1,â).
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Jun Liu, Dachun Yang, Wen Yuan,