Estimates of Weighted Hardy-Littlewood Inequality for Differential Forms

Abstract

Differential forms are interesting and important generalizations of real functions and distributions. Many interesting results and applications of differential forms have recently been found in some fields. As an important tool the Hardy-Littlewood inequality have been playing critical roles in many mathematics, including potential analysis, partial differential equations and the theory of elasticity.in this paper, the local and the global parametric weighted Hardy-Littlewood inequality had been proved on Riemannian manifolds by using the generalized weak reverse Holder inequality for A-harmonic tensors. The required versions can be obtained by selecting the suitable values for the parameters contained in each theorem. These results can be considered as generalizations of the classical Hardy-Littlewood inequality. As applications , the global versions of the Hardy-Littlewood inequality had been extended in L s -averaging domain and L s (w,l) averaging domain. Finally, the global parametric Hardy-Littlewood inequality for the projection operator had been obtained using the global weighted inequality for A -harmonic tensors. These results can also be used to study the integrability of differential forms and estimate the integrals for differential forms.