Molecular Characterizations Of Anisotropic Hardy Spaces With Variable Exponents And Their Applications

The real-variable theory of Hardy spaces plays an important role in harmonic anal-ysis,which has essential applications in various fields of analysis and partial differential equations.Let A be an expansive dilation on Rn,and p(·):Rn→(0,∞)be a variable exponent function satisfying the globally log-Holder continuous condition.Let HAp(·)(Rn)be the variable anisotropic Hardy space defined via the non-tangential grand maximal function.We mainly study the molecular decomposition of variable anisotropic Hardy space HAp(·)(Rn),which is still new even in the classical isotropic setting.As applications,we obtain the boundedness of anisotropic Calderon-Zygmund operators from HAp(·)(Rn)to LP(·)(Rn)or from HAp(·)(Rn)to itself.