Hardy-Littlewood Inequality For P-Harmonic Type Equation

IIn this paper, we consider the Hardy-Littlewood inequality for p-harmonic type equation. There are a lot of problem in science research and engineering technique relate to the differential system. The Hardy-Littlewood inequality is a useful tool in studying the solution of the differential system. Since 1932 when Hardy and Littlewood gave the classical Hardy-Littlewood inequality, many mathematics has extended it in many directions. For example, Hardy-Littlewood inequality has extended from analytic functions to conjugate Harmonic tensor; from regular domain in Euclidian space n to some special domain(such as John domain, Uniform domain, QED domain, Lip domain); from the classical norm to some special norm(such as Lip norm, BMO norm).The recent development was Hardy-Littlewood inequality for A-harmonic tensors which C. Nolder gave in 1999 and the weighted Hardy-Littlewood inequality for A-harmonic tensors which S. Ding gave in 1997.In this paper, we extend the A-harmonic e equation from the constant differential form which values in zero to any differential form, that is p-harmonic type equation. We extend some result of A-harmonic equation to p-harmonic type equation. At last we give the local result of Hardy-Littlewood inequality for p-harmonic type tensors, and the global result of Hardy-Littlewood inequality for p-harmonic type tensors on anyδ-John domain.