A noninequality for the fractional gradient

DOI10.4171/PM/2031zbMath1453.46035arXiv1906.05541MaRDI QIDQ2178384

Daniel E. Spector

Publication date: 11 May 2020

Published in: Portugaliae Mathematica. Nova Série (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1906.05541

zbMATH Keywords

trace inequalityLorentz spaces\(L^1\)-Sobolev inequality

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Inequalities involving derivatives and differential and integral operators (26D10) Harmonic analysis and PDEs (42B37)

Related Items (11)

Leibniz rules and Gauss-Green formulas in distributional fractional spaces ⋮ A distributional approach to fractional Sobolev spaces and fractional variation: asymptotics~II ⋮ Fractional Hardy-Sobolev \(L^1\)-embedding per capacity-duality ⋮ Failure of the local chain rule for the fractional variation ⋮ Fractional differential operators, fractional Sobolev spaces and fractional variation on homogeneous Carnot groups ⋮ Existence results for convection‐reaction fractional problem involving the distributional Riesz derivative ⋮ A trace inequality for solenoidal charges ⋮ A distributional approach to fractional Sobolev spaces and fractional variation: asymptotics. I ⋮ Endpoint \(L^1\) estimates for Hodge systems ⋮ New directions in harmonic analysis on \(L^1\) ⋮ The fractional variation and the precise representative of \(BV^{\alpha,p}\) functions

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