Maximal function characterizations of variable Hardy spaces associated with non-negative self-adjoint operators satisfying Gaussian estimates. (August 2016) - Zhuo, Ciqiang; Yang, Dachun
Abstract: Let p ( ⋅ ) : R n → ( 0, 1 ] be a variable exponent function satisfying the globally log -Hölder continuous condition and L a non-negative self-adjoint operator on L 2 ( R n ) whose heat kernels satisfying the Gaussian upper bound estimates. Let H L p ( ⋅ ) ( R n ) be the variable exponent Hardy space defined via the Lusin area function associated with the heat kernels { e − t 2 L } t ∈ ( 0, ∞ ) . In this article, the authors first establish the atomic characterization of H L p ( ⋅ ) ( R n ) ; using this, the authors then obtain its non-tangential maximal function characterization which, when p ( ⋅ ) is a constant in ( 0, 1 ], coincides with a recent result by L. Song and L. Yan (2016) and further induces the radial maximal function characterization of H L p ( ⋅ ) ( R n ) under an additional assumption that the heat kernels of L have the Hölder regularity.