Weighted inequalities for the fractional Laplacian and the existence of extremals

DOI10.1142/S0219199718500347zbMath1414.35256arXiv1705.00030MaRDI QIDQ5380165

Irene Drelichman, Pablo L. De Nápoli, Ariel Martin Salort

Publication date: 4 June 2019

Published in: Communications in Contemporary Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1705.00030

zbMATH Keywords

Sobolev spacesembedding theoremsextremalspower weightsfractional Laplacianpotential spaces

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Variational methods applied to PDEs (35A15) Fractional partial differential equations (35R11) Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals (35A23)

Related Items (3)

Fractional Calderón problems and Poincaré inequalities on unbounded domains ⋮ Existence of extremals of Dunkl-type Sobolev inequality and of Stein-Weiss inequality for Dunkl Riesz potential ⋮ Stein-Weiss inequality in 𝐿¹ norm for vector fields

Cites Work

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• Sharp constants in several inequalities on the Heisenberg group
• On Gagliardo-Nirenberg type inequalities
• Stein-Weiss and Caffarelli-Kohn-Nirenberg inequalities with angular integrability
• Fractional Gagliardo-Nirenberg and Hardy inequalities under Lorentz norms
• Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities
• Theory of function spaces
• On improved Sobolev embedding theorems
• Interpolation inequalities between Sobolev and Morrey-Campanato spaces: a common gateway to concentration-compactness and Gagliardo-Nirenberg interpolation inequalities
• Fractional Sobolev-Hardy inequality in \(\mathbb{R}^N\)
• Regularity criteria with angular integrability for the Navier-Stokes equation
• Improved Sobolev embeddings, profile decomposition, and concentration-compactness for fractional Sobolev spaces
• A New, Rearrangement-free Proof of the Sharp Hardy–Littlewood–Sobolev Inequality
• A Relation Between Pointwise Convergence of Functions and Convergence of Functionals
• Temperatures, Bessel Potentials and Lipschitz Spaces
• Weighted Norm Inequalities for the Hardy Maximal Function

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