𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Estimates of Weighted Integrals for Differential Forms

✍ Scribed by Shusen Ding

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
105 KB
Volume
256
Category
Article
ISSN
0022-247X

No coin nor oath required. For personal study only.

✦ Synopsis

In this paper we obtain some weighted integral estimates for differential forms which are generalizations of the Poincaré inequality, the Caccioppoli-type estimate, and the weak reverse Hölder inequality, respectively. These results can be used to study the integrability of differential forms and to estimate the integrals for differential forms.

📜 SIMILAR VOLUMES

Differential Forms and the Change of Var
Differential Forms and the Change of Variable Formula for Multiple Integrals
✍ Michael Taylor 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 67 KB

Recently P. Lax has produced a novel approach to the proof of the change of variable formula for multiple integrals. In Section 1 we give a variant of Lax's proof, using the language of differential forms. In Sections 2 and 3 we discuss extensions involving more singular maps and integrands.  2002

Weighted Imbedding Theorems in the Space
Weighted Imbedding Theorems in the Space of Differential Forms
✍ Shusen Ding 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 101 KB

We prove A r -weighted imbedding theorems for differential forms. These results can be used to study the weighted norms of the homotopy operator T from the Banach space L p D ∧ l to the Sobolev space W 1 p D ∧ l-1 l = 1 2 n, and to establish the basic weighted L p -estimates for differential forms.

Weighted Sobolev L2 estimates for a clas
Weighted Sobolev L2 estimates for a class of Fourier integral operators
✍ Michael Ruzhansky; Mitsuru Sugimoto 📂 Article 📅 2011 🏛 John Wiley and Sons 🌐 English ⚖ 235 KB 👁 1 views

In this paper we develop elements of the global calculus of Fourier integral operators in R n under minimal decay assumptions on phases and amplitudes. We also establish global weighted Sobolev L 2 estimates for a class of Fourier integral operators that appears in the analysis of global smoothing p

Sharp differential estimates of Li-Yau-H
Sharp differential estimates of Li-Yau-Hamilton type for positive (p, p) forms on Kähler manifolds
✍ Lei Ni; Yanyan Niu 📂 Article 📅 2011 🏛 John Wiley and Sons 🌐 English ⚖ 405 KB

## Abstract In this paper we study the heat equation (of Hodge Laplacian) deformation of (__p, p__)‐forms on a Kähler manifold. After identifying the condition and establishing that the positivity of a (__p, p__)‐form solution is preserved under such an invariant condition, we prove the sharp diffe

Lipschitz estimates for generalized comm
Lipschitz estimates for generalized commutators of fractional integrals with rough kernel
✍ Shanzhen Lu; Pu Zhang 📂 Article 📅 2003 🏛 John Wiley and Sons 🌐 English ⚖ 214 KB

## Abstract Let $ T ^{A} \_{\Omega, \alpha} $ (0 < __α__ < __n__) be the generalized commutator generated by fractional integral with rough kernel and the __m__–th order remainder of the Taylor formula of a function A. In this paper, the (__L__^__p__^, __L__^__r__^) (__r__ > 1) boundedness, the wea