Anisotropic variable Hardy-Lorentz spaces and their real interpolation

作者：Liu Jun; Yang Dachun^*; Yuan Wen

来源：Journal of Mathematical Analysis and Applications, 2017, 456(1): 356-393.

DOI：10.1080/0023131.2017.07.003

• Variable exponent
• (Hardy-) Lorentz space
• Expansive matrix
• Atom
• Lusin area function
• Real interpolation

Let p(.) : R-n -> (0, infinity] be a variable exponent function satisfying the globally log-Holder continuous condition, q is an element of (0, infinity] and A be a general expansive matrix on R-n. In this article, the authors first introduce the anisotropic variable Hardy-Lorentz space H-A(p(.),q) (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(.),q) (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(.),q) (R-n) serves as the intermediate space between the anisotropic variable Hardy space H-A(p(.),q) (R-n) and the space L-infinity (R-n) via the real interpolation. This, together with a special case of the real interpolation theorem of H. Kempka and J. Vybfral on the variable Lorentz space, further implies the coincidence between H-A(p(.),q) (R-n) and the variable Lorentz space R-Lp(.),R-q()(n) when ess inf(x is an element of Rn) p(x) is an element of (1, infinity).

• 出版日期2017-12-1
• 单位北京师范大学