Compactness, interpolation inequalities for small Lebesgue-Sobolev spaces and applications

DOI10.1007/s00526-005-0346-5zbMath1098.46025OpenAlexW2162427062MaRDI QIDQ818995

Alberto Fiorenza, Jean Michel Rakotoson

Publication date: 22 March 2006

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00526-005-0346-5

zbMATH Keywords

small Lebesgue spaces, Sobolev spaces, compact embeddings, variational problems

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) Nonlinear elliptic equations (35J60) Interpolation between normed linear spaces (46B70) Inequalities involving other types of functions (26D07)

Related Items (16)

On Hardy type inequalities in grand Lebesgue spacesL_p)for 0 <p≤ 1 ⋮ Characterization of interpolation between grand, small or classical Lebesgue spaces ⋮ Boundedness of some singular integrals operators in weighted generalized Grand Lebesgue spaces ⋮ Variable exponents and grand Lebesgue spaces: Some optimal results ⋮ Fully measurable small Lebesgue spaces ⋮ Characterization of associate spaces of weighted Lorentz spaces with applications ⋮ On grand and small Lebesgue and Sobolev spaces and some applications to PDE's ⋮ Embeddings of Lorentz-type spaces involving weighted integral means ⋮ Real interpolation of small Lebesgue spaces in a critical case ⋮ Grand Lebesgue spaces with respect to measurable functions ⋮ On the solvability of nonlinear ordinary differential equations in grand Lebesgue spaces ⋮ Sobolev anisotropic inequalities with monomial weights ⋮ Some estimates in \(G\Gamma (p,m,w)\) spaces ⋮ Boundedness of classical operators on rearrangement-invariant spaces ⋮ A direct approach to the duality of grand and small Lebesgue spaces ⋮ Linear equation with data in non standard spaces

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