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Orlicz spaces of differential forms on Riemannian manifolds : Duality and cohomology. / Kopylov, Ya A.

In: Problemy Analiza, Vol. 6, No. 2, 01.01.2017, p. 57-80.

Research output: Contribution to journal › Article › peer-review

Harvard

Kopylov, YA 2017, 'Orlicz spaces of differential forms on Riemannian manifolds: Duality and cohomology', Problemy Analiza, vol. 6, no. 2, pp. 57-80. https://doi.org/10.15393/j3.art.2017.3850

APA

Kopylov, Y. A. (2017). Orlicz spaces of differential forms on Riemannian manifolds: Duality and cohomology. Problemy Analiza, 6(2), 57-80. https://doi.org/10.15393/j3.art.2017.3850

Vancouver

Kopylov YA. Orlicz spaces of differential forms on Riemannian manifolds: Duality and cohomology. Problemy Analiza. 2017 Jan 1;6(2):57-80. doi: 10.15393/j3.art.2017.3850

Author

Kopylov, Ya A. / Orlicz spaces of differential forms on Riemannian manifolds : Duality and cohomology. In: Problemy Analiza. 2017 ; Vol. 6, No. 2. pp. 57-80.

BibTeX

@article{79ccb7b220604ad287e12b9d625c57b4,
title = "Orlicz spaces of differential forms on Riemannian manifolds: Duality and cohomology",
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 H{\"o}lder-Poincar{\'e} duality for reduced Lq,p-cohomology by Gol0dshtein and Troyanov to LΦI, ΦII -cohomology, where ΦI and ΦII are N-functions of class Δ2 ∩ ∇2.",
keywords = "Differential form, Exterior differential, Orlicz cohomology, Orlicz space, Riemannian manifold, differential form, exterior differential, L2-COHOMOLOGY, LP-COHOMOLOGY",
author = "Kopylov, {Ya A.}",
year = "2017",
month = jan,
day = "1",
doi = "10.15393/j3.art.2017.3850",
language = "English",
volume = "6",
pages = "57--80",
journal = "Problemy Analiza",
issn = "2306-3424",
publisher = "Petrozavodsk State University",
number = "2",

}

RIS

TY - JOUR

T1 - Orlicz spaces of differential forms on Riemannian manifolds

T2 - Duality and cohomology

AU - Kopylov, Ya A.

PY - 2017/1/1

Y1 - 2017/1/1

N2 - 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-Poincaré duality for reduced Lq,p-cohomology by Gol0dshtein and Troyanov to LΦI, ΦII -cohomology, where ΦI and ΦII are N-functions of class Δ2 ∩ ∇2.

AB - 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-Poincaré duality for reduced Lq,p-cohomology by Gol0dshtein and Troyanov to LΦI, ΦII -cohomology, where ΦI and ΦII are N-functions of class Δ2 ∩ ∇2.

KW - Differential form

KW - Exterior differential

KW - Orlicz cohomology

KW - Orlicz space

KW - Riemannian manifold

KW - differential form

KW - exterior differential

KW - L2-COHOMOLOGY

KW - LP-COHOMOLOGY

UR - http://www.scopus.com/inward/record.url?scp=85040698484&partnerID=8YFLogxK

U2 - 10.15393/j3.art.2017.3850

DO - 10.15393/j3.art.2017.3850

M3 - Article

AN - SCOPUS:85040698484

VL - 6

SP - 57

EP - 80

JO - Problemy Analiza

JF - Problemy Analiza

SN - 2306-3424

IS - 2

ER -

ID: 10455352