Integral isoperimetric transference and dimensionless Sobolev inequalities

DOI10.1007/s13163-014-0153-7zbMath1338.46038arXiv1309.1980OpenAlexW3099117507MaRDI QIDQ2348347

Mario Milman, Joaquim Martín

Publication date: 12 June 2015

Published in: Revista Matemática Complutense (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1309.1980

zbMATH Keywords

symmetrizationisoperimetric inequalitiesextrapolationSobolev inequalities

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) Inequalities involving derivatives and differential and integral operators (26D10)

Related Items

On grand and small Lebesgue and Sobolev spaces and some applications to PDE's, A local estimate for the maximal function in Lebesgue spaces with EXP-type exponents

Cites Work

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• On dimension-free Sobolev imbeddings. II
• On dimension-free Sobolev imbeddings. I.
• Pointwise symmetrization inequalities for Sobolev functions and applications
• The computation of the K functional for couples of rearrangement invariant spaces
• On the integrability of the Jacobian under minimal hypotheses
• Best constant in Sobolev inequality
• A mass-transportation approach to sharp Sobolev and Gagliardo-Nirenberg inequalities.
• Duality and reflexivity in grand Lebesgue spaces
• Log-concave and spherical models in isoperimetry
• Grand and small Lebesgue spaces and their analogs
• Extrapolation theory: new results and applications
• Complemented Brunn-Minkowski inequalities and isoperimetry for homogeneous and non-homogeneous measures
• An improvement of dimension-free Sobolev imbeddings in r.i. spaces
• Monotonicity of certain functionals under rearrangement
• Sobolev inequalities: symmetrization and self-improvement via truncation
• Tractable embeddings of Besov spaces into Zygmund spaces
• Sobolev inequalities, rearrangements, isoperimetry and interpolation spaces
• Some connections between isoperimetric and Sobolev-type inequalities
• Fractional Sobolev Inequalities: Symmetrization, Isoperimetry and Interpolation
• A Converse to the Maz’ya Inequality for Capacities under Curvature Lower Bound
• Indices of Function Spaces and their Relationship to Interpolation