Remarks on the Fractional Moser—Trudinger Inequality

In this article, we study the connection between the fractional Moser—Trudinger inequality and the fractional ( k p p − 1 , p )-Poincaré type inequality for any Euclidean domain and discuss the sharpness of this inequality whose analogous results are well known in the local case. We further provide...

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Bibliographic Details
Published inJournal d'analyse mathématique (Jerusalem) Vol. 148; no. 2; pp. 447 - 470
Main Author Sk, Firoj
Format Journal Article
LanguageEnglish
Published Jerusalem The Hebrew University Magnes Press 01.12.2022
Springer Nature B.V
Subjects
Abstract Harmonic Analysis
Analysis
Domains
Dynamical Systems and Ergodic Theory
Functional Analysis
Inequalities
Mathematics
Mathematics and Statistics
Partial Differential Equations
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Summary:In this article, we study the connection between the fractional Moser—Trudinger inequality and the fractional ( k p p − 1 , p )-Poincaré type inequality for any Euclidean domain and discuss the sharpness of this inequality whose analogous results are well known in the local case. We further provide sufficient conditions on domains for fractional ( q, p )-Porncaré type inequalities to hold. We also derive Adachi—Tanaka type inequalities in the non-local setting.
ISSN:0021-7670
1565-8538
DOI:10.1007/s11854-022-0234-3