Elementary reverse Hölder type inequalities with application to operator interpolation theory

DOI10.1090/S0002-9939-96-03651-9zbMath0865.46015OpenAlexW1568652439MaRDI QIDQ4717090

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Publication date: 13 July 1997

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-96-03651-9

zbMATH Keywords

Hardy operatorCalderón operatorboundedness on \(L^ p\)classes of weightsintermediate interpolation spacesinterpolation for general Lorentz spacesreverse Hölder type inequality

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) Interpolation between normed linear spaces (46B70) Abstract interpolation of topological vector spaces (46M35)

Related Items (4)

Characterization of interpolation between grand, small or classical Lebesgue spaces ⋮ On grand and small Lebesgue and Sobolev spaces and some applications to PDE's ⋮ Lebesgue's differentiation theorems in r.i. quasi-Banach spaces and Lorentz spaces \(\Gamma_{p,w}\) ⋮ \(S\)-divisibility property and a Holmstedt type formula

Cites Work

• K-divisibility of the K-functional and Calderón couples
• Interpolation of operators of weak type
• Weighted norm inequalities for averaging operators of monotone functions
• Maximal Functions on Classical Lorentz Spaces and Hardy's Inequality with Weights for Nonincreasing Functions
• On Hardy's Inequality in Weighted Rearrangement Invariant Spaces and Applications. I
• Boundedness of classical operators on classical Lorentz spaces
• Interpolation of operators when the extreme spaces are $L^{∞}$
• Calderón couples of rearrangement invariant spaces
• Weighted Norm Inequalities for the Hardy Maximal Function
• Majorants in Spaces of Integrable Functions
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