Characterizations Of Hardy Spaces Associated To Higher Order Elliptic Operators

This paper defines the Hardy space HLP(Rn)related to operator L, where L is a higher order divergence form elliptic operator with complex bounded measurable coefficients,and according to the area integrations related to the two half groups e-tL and e-t(?), who show the the characterization of Hardy space HLP(Rn) by analytic and non-diagonal estimate of higher-order relation to heat semigroup e-tL This dissertation is organized as follows:Chapter 1 introduces some background about the Hardy space HLP(Rn). In chapter 2, around the half group generated by higher order divergence form elliptic operator with complex bounded measurable coefficients, the authors describe the definition of Hardy space HLP(Rn) and produce Ls-Lq estimates relating to semigroups, and the boundedness of square functions. In chapter 3, mainly introduced the definition of molecular Hardy spaces HLP(Rn) ,0<p≤1.At the same time we prove the Hardy space HLP(Rn) is equivalent to HLP(Rn). In chapter 4, which is regarded as the core sections of this paper, the main basis of the previous chapters discusses the characterizations of Hardy space HLP(Rn),0< p< 1, focusing on two types of area integral ShL,k and Sp’k. In chapter 5, the authors the application of the (HLP,Lp) boundedess of vertical maximal operator.