MAXIMAL FUNCTION CHARACTERIZATIONS OF HARDY SPACES ASSOCIATED WITH BOTH NON-NEGATIVE SELF-ADJOINT OPERATORS SATISFYING GAUSSIAN ESTIMATES AND BALL QUASI-BANACH FUNCTION SPACES

【摘要】 Assume that L is a non-negative self-adjoint operator on L²（Rⁿ） with its heat kernels satisfying the so-called Gaussian upper bound estimate and that X is a ball quasiBanach function space on Rⁿ satisfying some mild assumptions.Let H_X,L（Rⁿ） be the Hardy space associated with both X and L,which is defined by the Lusin area function related to the semigroup generated by L.In this article,the authors establish various maximal function characterizations of the Hardy space H_X,L（Rⁿ） and then apply these characterizations to obtain the solvability of the related Cauchy problem.These results have a wide range of generality and,in particular,the specific spaces X to which these results can be applied include the weighted space,the variable space,the mixed-norm space,the Orlicz space,the Orlicz-slice space,and the Morrey space.Moreover,the obtained maximal function characterizations of the mixed-norm Hardy space,the Orlicz-slice Hardy space,and the Morrey-Hardy space associated with L are completely new.更多还原

【Abstract】 Assume that L is a non-negative self-adjoint operator on L²（Rⁿ） with its heat kernels satisfying the so-called Gaussian upper bound estimate and that X is a ball quasiBanach function space on Rⁿ satisfying some mild assumptions.Let H_X,L（Rⁿ） be the Hardy space associated with both X and L,which is defined by the Lusin area function related to the semigroup generated by L.In this article,the authors establish various maximal function characterizations of the Hardy space H_X,L（Rⁿ） and then apply these characterizations to obtain the solvability of the related Cauchy problem.These results have a wide range of generality and,in particular,the specific spaces X to which these results can be applied include the weighted space,the variable space,the mixed-norm space,the Orlicz space,the Orlicz-slice space,and the Morrey space.Moreover,the obtained maximal function characterizations of the mixed-norm Hardy space,the Orlicz-slice Hardy space,and the Morrey-Hardy space associated with L are completely new.更多还原