ORLICZ SPACES OF DIFFERENTIAL FORMS ON RIEMANNIAN MANIFOLDS: DUALITY AND COHOMOLOGY
Journal Title: Проблемы анализа-Issues of Analysis - Year 2017, Vol 6, Issue 2
Abstract
We consider Orlicz spaces of differential forms on a Riemannian manifold. A Riesz-type theorem about the functionals on Orlicz spaces of forms is proved and other duality theorems are obtained therefrom. We also extend the results on the Hölder-Poincarè duality for reduced L_q,_p-cohomology by Gol`dshtein and Troyanov to Lᵩᵢ ,ᵩᵢᵢ -cohomology, where Φᵢ and Φᵢᵢ are N-functions of class ∆2 ∩ ∇2.
Authors and Affiliations
Ya. A. Kopylov
Keywords
Related Articles
- EP ID EP227115
- DOI 10.15393/j3.art.2017.3850
- Views 100
- Downloads 0
ON THE PROJECTIONS OF MUTUAL L^{q,t}-SPECTRUM
In this paper we are interested in the mutual L^{q,t}-spectrum relatively to two Borel probability measures having the same compact support and also in the study of their behavior under orthogonal projections.
N-FRACTIONAL CALCULUS OPERATOR METHOD TO THE EULER EQUATION
We can obtain the explicit solutions of the Euler equation by using the fractional calculus methods. So, we apply the N operator method in the fractional calculus to solve this equation in this paper. We take advantage o...
THE DAMASCUS INEQUALITY
In 2016 Prof. Fozi M. Dannan from Damascus, Syria, proposed an interesting inequality for three positive numbers with unit product. It became widely known but was not proved yet in spite of elementary formulation. In thi...
ПЕРЕСЕЧЕНИЕ МНОЖЕСТВА ЭКСТРЕМАЛЬНЫХ ФУНКЦИЙ ДЛЯ ДВУХ ФУНКЦИОНАЛОВ
В работе исследована экстремальная задача для линейного функционала в классе U' α. В частности, получен вид экстремальной функции.
INEQUALITIES CONNECTING GENERALIZED TRIGONOMETRIC FUNCTIONS WITH THEIR INVERSES
Motivated by the recent work [1], in this paper we study the relations of generalized trigonometric and hyperbolic functions of two parameters with their inverse functions.