Resumen de Atomic and maximal function characterizations of Musielak–Orlicz–Hardy spaces associated to non-negative self-adjoint operators on spaces of homogeneous type
Sibei Yang, Dachun Yang
Let be a metric space with doubling measure and L be a non-negative self-adjoint operator on ?2() whose heat kernels satisfy the Gaussian upper bound estimates. Assume that the growth function ?: ×[0,∞)→[0,∞) satisfies that ?(?,⋅) is an Orlicz function and ?(⋅,?)∈?∞() (the class of uniformly Muckenhoupt weights). Let ??,?() be the Musielak–Orlicz–Hardy space defined via the Lusin area function associated with the heat semigroup of L. In this article, the authors characterize the space ??,?() by means of atoms, non-tangential and radial maximal functions associated with L. In particular, when ?()<∞ , the local non-tangential and radial maximal function characterizations of ??,?() are obtained. As applications, the authors obtain various maximal function and the atomic characterizations of the “geometric” Musielak–Orlicz–Hardy spaces ??,?(Ω) and ??,?(Ω) on the strongly Lipschitz domain Ω in ℝ? associated with second-order self-adjoint elliptic operators with the Dirichlet and the Neumann boundary conditions; even when ?(?,?):=? for any ?∈ℝ? and ?∈[0,∞) , the equivalent characterizations of ??,?(Ω) given in this article improve the known results via removing the assumption that Ω is unbounded.
