Displaying similar documents to “Relative rearrangement and interpolation inequalities.”

Weighted inequalities for monotone functions.

L. Maligranda (1997)

Collectanea Mathematica

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We give characterizations of weights for which reverse inequalities of the Hölder type for monotone functions are satisfied. Our inequalities with general weights and with sharp constants complement previous results.

Sobolev spaces on multiple cones

P. Auscher, N. Badr (2010)

Annales de la faculté des sciences de Toulouse Mathématiques

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The purpose of this note is to discuss how various Sobolev spaces defined on multiple cones behave with respect to density of smooth functions, interpolation and extension/restriction to/from ℝ n . The analysis interestingly combines use of Poincaré inequalities and of some Hardy type inequalities.

Sobolev-Kantorovich Inequalities

Michel Ledoux (2015)

Analysis and Geometry in Metric Spaces

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In a recent work, E. Cinti and F. Otto established some new interpolation inequalities in the study of pattern formation, bounding the Lr(μ)-norm of a probability density with respect to the reference measure μ by its Sobolev norm and the Kantorovich-Wasserstein distance to μ. This article emphasizes this family of interpolation inequalities, called Sobolev-Kantorovich inequalities, which may be established in the rather large setting of non-negatively curved (weighted) Riemannian manifolds...

Transferring monotonicity in weighted norm inequalities.

Gord Sinnamon (2003)

Collectanea Mathematica

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Certain weighted norm inequalities for integral operators with non-negative, monotone kernels are shown to remain valid when the weight is replaced by a monotone majorant or minorant of the original weight. A similar result holds for operators with quasi-concave kernels. To prove these results a careful investigation of the functional properties of the monotone envelopes of a non-negative function is carried-out. Applications are made to function space embeddings of the cones of monotone...

Comparison theorems of isoperimetric type for moments of compact sets.

F. G. Avkhadiev, I. R. Kayumov (2004)

Collectanea Mathematica

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A unified approach to prove isoperimetric inequalities for moments and basic inequalities of interpolation spaces L(p,q) is developed. Instead symmetrization methods we use a monotonicity property of special Stiltjes' means.