The Bourgain-Brézis-Mironescu formula in arbitrary bounded domains

DOI10.1090/proc/15665zbMath1484.46036arXiv2012.14505OpenAlexW3160372938MaRDI QIDQ5020709

Irene Drelichman, Ricardo G. Durán

Publication date: 7 January 2022

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2012.14505

zbMATH Keywords

Sobolev spacesreal interpolationbounded domains

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Fractional derivatives and integrals (26A33) Interpolation between normed linear spaces (46B70) Inequalities involving derivatives and differential and integral operators (26D10)

Related Items (3)

Weighted fractional Sobolev spaces as interpolation spaces in bounded domains ⋮ Self-improving Poincaré-Sobolev type functionals in product spaces ⋮ Bourgain-Brezis-Mironescu formula for \(W^{s, p}_q\)-spaces in arbitrary domains

Cites Work

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• On the Bourgain, Brezis, and Mironescu theorem concerning limiting embeddings of fractional Sobolev spaces
• Fractional Sobolev-Poincaré inequalities in irregular domains
• A T(1) theorem for fractional Sobolev spaces on domains
• Corrigendum to ``Characterization of Sobolev and \(BV\) spaces
• On comparability of integral forms
• Notes on limits of Sobolev spaces and the continuity of interpolation scales
• Improved Poincar\'e inequalities in fractional Sobolev spaces
• Estimates for singular integral operators in terms of maximal functions
• H = W

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