Estimates of Weighted Hardy-Littlewood Inequality for Differential Forms

نویسنده

  • Haijing Zhu
چکیده

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 Ls-averaging domain and Ls (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.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Hardy–Littlewood–Sobolev and Stein–Weiss inequalities and integral systems on the Heisenberg group

In this paper, we study two types of weighted Hardy–Littlewood–Sobolev (HLS) inequalities, also known as Stein–Weiss inequalities, on the Heisenberg group. More precisely, we prove the |u| weighted HLS inequality in Theorem 1.1 and the |z| weighted HLS inequality in Theorem 1.5 (where we have denoted u = (z, t) as points on the Heisenberg group). Then we provide regularity estimates of positive...

متن کامل

Extension of Hardy Inequality on Weighted Sequence Spaces

Let and be a sequence with non-negative entries. If , denote by the infimum of those satisfying the following inequality: whenever . The purpose of this paper is to give an upper bound for the norm of operator T on weighted sequence spaces d(w,p) and lp(w) and also e(w,?). We considered this problem for certain matrix operators such as Norlund, Weighted mean, Ceasaro and Copson ma...

متن کامل

Global Caccioppoli-Type and Poincaré Inequalities with Orlicz Norms

The L-theory of solutions of the homogeneous A-harmonic equation d A x, dω 0 for differential forms has been very well developed in recent years. Many L-norm estimates and inequalities, including the Hardy-Littlewood inequalities, Poincaré inequalities, Caccioppoli-type estimates, and Sobolev imbedding inequalities, for solutions of the homogeneous A-harmonic equation have been established; see...

متن کامل

On a new Hardy-Littlewood-Polya’s inequality with multi-parameters and its applications

(1.1) and (1.2) is the well known Hardy-Littlewood-Polya’s inequality. In connection with applications in analysis, their generalizations and variants have received considerable interest recent years. Firstly, by means of introducing a parameter, two forms of extended Hardy-Littlewood-Polya’s inequality are obtained by Hu in [2] as follows. (1) Let λ > 0, p > 1, 1 p+ 1 q=1, f(x), g(y) ≥ 0, F (x...

متن کامل

0 M ay 2 00 9 PITT ’ S INEQUALITY AND THE FRACTIONAL LAPLACIAN : SHARP ERROR ESTIMATES for

Considerable interest exists in understanding the framework of weighted inequalities for differential operators and the Fourier transform, and the application of quantitative information drawn from these inequalities to varied problems in analysis and mathematical physics, including nonlinear partial differential equations, spectral theory, fluid mechanics, stability of matter, stellar dynamics...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • JNW

دوره 8  شماره 

صفحات  -

تاریخ انتشار 2013