Two-Weighted Intergal Inequalities for Differential Forms

New Weighted Integral Inequalities for Differential Forms in Some Domains

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, such as tensor analysis, potential theory, partial differential equations and quasiregular mappings, see [B], [C], [D1], [HKM], [I], [IL] and [IM]. In many cases, we need to know the integra...

Weighted Inequalities for Potential Operators on Differential Forms

Weighted Decomposition Estimates for Differential Forms

Let e1, e2, . . . , en denote the standard orthogonal basis of R. Suppose that Λ Λ R is the linear space of all l-vectors, spanned by the exterior product eI ei1∧ei2∧· · ·∧eil corresponding to all ordered l-tuples I i1, i2, . . . , il , 1 ≤ i1 < i2 < · · · < il ≤ n. Throughout this paper, we always assume that Ω is an open subset of R. We use D′ M,Λ to denote the space of all differential l-for...

Novikov Type Inequalities for Differential Forms with Non-isolated Zeros

We generalize the Novikov inequalities for 1-forms in two different directions: first, we allow non-isolated critical points (assuming that they are nondegenerate in the sense of R.Bott), and, secondly, we strengthen the inequalities by means of twisting by an arbitrary flat bundle. The proof uses Bismut’s modification of the Witten deformation of the de Rham complex; it is based on an explicit...

Two-weight Poincaré-type inequalities for differential forms in Ls(µ)-averaging domains

We establish the local and global two-weight Poincaré inequalities for differential forms in Ls(μ)-averaging domains. c © 2007 Elsevier Ltd. All rights reserved.