Rearrangement-function inequalities and interpolation theory

DOI10.1006/jath.2002.3730zbMath1032.46045OpenAlexW1971556209MaRDI QIDQ1867521

Yoram Sagher, Pavel Shvartsman

Publication date: 2 April 2003

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jath.2002.3730

zbMATH Keywords

rearrangementsreal interpolation\(BMO\)weak type

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) Linear operators on function spaces (general) (47B38) Inequalities in approximation (Bernstein, Jackson, Nikol'ski?-type inequalities) (41A17) Abstract interpolation of topological vector spaces (46M35)

Related Items (7)

BMO: Oscillations, Self-Improvement, Gagliardo Coordinate Spaces, and Reverse Hardy Inequalities ⋮ ON SHARP HIGHER ORDER SOBOLEV EMBEDDINGS ⋮ New estimates for the maximal functions and applications ⋮ Characterization of a rearrangement-invariant hull of a Besov space via interpolation ⋮ A new look at the John-Nirenberg and John-Strömberg theorems for BMO ⋮ The modulus of smoothness in metric spaces and related problems ⋮ Pointwise symmetrization inequalities for Sobolev functions and applications

Cites Work

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• Local sharp maximal functions
• Weak-\(L^\infty\) and BMO
• Weighted Hardy spaces
• Maximal functions with respect to differential bases measuring mean oscillation
• An interpolation theorem with perturbed continuity
• Interpolation of normed Abelian groups
• Covering Lemmas and the Sharp Function
• A Rearranged Good λ Inequality
• Weighted norm inequalities for maximal functions and singular integrals
• Weak*-sequential closure and the characteristic of subspaces of conjugate Banach spaces
• The approximation functional and interpolation with perturbed continuity

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