Optimality of Function Spaces in Sobolev Embeddings

DOI10.1007/978-0-387-85648-3_9zbMath1166.46016OpenAlexW181439177MaRDI QIDQ3613585

Luboš Pick

Publication date: 12 March 2009

Published in: Sobolev Spaces In Mathematics I (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-0-387-85648-3_9

zbMATH Keywords

Sobolev embeddingsoptimalityinterpolation theorySobolev inequalitiesrearrangement-invariant Banach function spaces

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) Research exposition (monographs, survey articles) pertaining to functional analysis (46-02)

Related Items (5)

Continuous and Compact Embeddings of Bessel-Potential-Type Spaces ⋮ Embeddings, Hardy operators and nonlinear problems ⋮ An improvement of dimension-free Sobolev imbeddings in r.i. spaces ⋮ Weighted Inequalities for Integral and Supremum Operators ⋮ Optimal Gaussian Sobolev embeddings

Cites Work

• Weighted inequalities for Hardy-type operators involving suprema
• Boundary trace inequalities and rearrangements
• Optimal Gaussian Sobolev embeddings
• Interpolation of linear operators on Sobolev spaces
• Weak-\(L^\infty\) and BMO
• Best constant in Sobolev inequality
• Optimal Orlicz-Sobolev embeddings
• Optimal Sobolev imbeddings involving rearrangement-invariant quasinorms
• Weak type interpolation near ``endpoint spaces
• The free Markoff field
• On the Brudnyĭ-Krugljak duality theory of spaces formed by the \(\mathcal K\)-method of interpolation
• Symmetrization and second-order Sobolev inequalities
• Espaces d'interpolation et théorème de Soboleff
• Convolution operators and L(p, q) spaces
• On L(p,q) spaces
• Functional properties of rearrangement invariant spaces defined in terms of oscillations
• An elementary proof of sharp Sobolev embeddings
• Explicit formulas for optimal rearrangement-invariant norms in Sobolev imbedding inequalities
• Optimal Sobolev imbeddings
• Boundedness of classical operators on classical Lorentz spaces
• A note on limiting cases of sobolev embeddings and convolution inequalities
• Logarithmic Sobolev Inequalities
• A sharp embedding theorem for Orlicz-Sobolev spaces
• Interpolation of Operators on Scales of Generalized Lorentz-Zygmund Spaces
• Are generalized Lorentz “spaces” really spaces?
• Compactness of Sobolev imbeddings involving rearrangement-invariant norms
• Interpolation of Quasi-Normed Spaces.
• On the sharpness of a limiting case of the Sobolev imbedding theorem
• A note on L(\infty, q) spaces and Sobolev embeddings
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