Optimal interpolation in spaces of Lorentz-Zygmund type

DOI10.1007/BF02788238zbMath0987.46035MaRDI QIDQ5943730

Evgeniy Pustylnik

Publication date: 17 September 2001

Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)

zbMATH Keywords

rearrangement invariant spaceembeddingsequivalencesBoyd indicesfundamental functionsLorentz-Zygmund 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) Linear operators on function spaces (general) (47B38) Interpolation between normed linear spaces (46B70) Abstract interpolation of topological vector spaces (46M35)

Related Items (16)

General reiteration theorems for \(\mathcal{R}\) and \(\mathcal{L}\) classes: mixed interpolation of \(\mathcal{R}\) and \(\mathcal{L}\)-spaces ⋮ Generalized fractional maximal functions in Lorentz spaces Λ ⋮ General reiteration theorems for \(\mathcal{R}\) and \(\mathcal{L}\) classes: case of right \(\mathcal{R}\)-spaces and left \(\mathcal{L}\)-spaces ⋮ Weighted inequalities for discrete iterated kernel operators ⋮ Absolutely continuous embeddings of rearrangement-invariant spaces ⋮ The supremum-involving Hardy-type operators on Lorentz-type spaces ⋮ Unnamed Item ⋮ On a rearrangement-invariant function set that appears in optimal Sobolev embeddings ⋮ Orbits and co-orbits of ultrasymmetric spaces in weak interpolation ⋮ Dual spaces of Lorentz-Zygmund type in optimal interpolation ⋮ Weighted Inequalities for Integral and Supremum Operators ⋮ Reiteration theorem for \(\mathcal{R}\) and \(\mathcal{L}\)-spaces with the same parameter ⋮ A sharp blow-up estimate for the Lebesgue norm ⋮ Boundedness of weighted iterated Hardy-type operators involving suprema from weighted Lebesgue spaces into weighted Cesàro function spaces ⋮ On compactness of Sobolev embeddings in rearrangement-invariant spaces ⋮ Extreme cases of weak type interpolation

Cites Work

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• Weak type interpolation near ``endpoint spaces
• Interpolation spaces and interpolation methods
• Counterexamples for classical operators on Lorentz-Zygmund spaces
• Minimal and maximal intermediate Banach spaces
• Interpolation of Operators on Scales of Generalized Lorentz-Zygmund Spaces
• Double exponential integrability of convolution operators in generalized Lorentz-Zygmund spaces
• Weak*-sequential closure and the characteristic of subspaces of conjugate Banach spaces
• Interpolation of Quasi-Normed Spaces.

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