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Linearization and compactness

Jesús Ángel Jaramillo, Ángeles Prieto, Ignacio Zalduendo (2009)

Studia Mathematica

This paper is devoted to several questions concerning linearizations of function spaces. We first consider the relation between linearizations of a given space when it is viewed as a function space over different domains. Then we study the problem of characterizing when a Banach function space admits a Banach linearization in a natural way. Finally, we consider the relevance of compactness properties in linearizations, more precisely, the relation between different compactness properties of a mapping,...

Lipschitz approximable Banach spaces

Gilles Godefroy (2020)

Commentationes Mathematicae Universitatis Carolinae

We show the existence of Lipschitz approximable separable spaces which fail Grothendieck's approximation property. This follows from the observation that any separable space with the metric compact approximation property is Lipschitz approximable. Some related results are spelled out.

Lipschitz continuity in Muckenhoupt 𝓐₁ weighted function spaces

Dorothee D. Haroske (2011)

Banach Center Publications

We study continuity envelopes of function spaces B p , q s ( ℝ ⁿ , w ) and F p , q s ( ℝ ⁿ , w ) where the weight belongs to the Muckenhoupt class ₁. This essentially extends partial forerunners in [13, 14]. We also indicate some applications of these results.

Lipschitz spaces and Calderón-Zygmund operators associated to non-doubling measures.

José García-Cuerva, A. Eduardo Gatto (2005)

Publicacions Matemàtiques

In the setting of a metric measure space (X, d, μ) with an n-dimensional Radon measure μ, we give a necessary and sufficient condition for the boundedness of Calderón-Zygmund operators associated to the measure μ on Lipschitz spaces on the support of μ. Also, for the Euclidean space Rd with an arbitrary Radon measure μ, we give several characterizations of Lipschitz spaces on the support of μ, Lip(α,μ), in terms of mean oscillations involving μ. This allows us to view the "regular" BMO space of...

Lipschitzian norm estimate of one-dimensional Poisson equations and applications

Hacene Djellout, Liming Wu (2011)

Annales de l'I.H.P. Probabilités et statistiques

By direct calculus we identify explicitly the lipschitzian norm of the solution of the Poisson equation in terms of various norms of g, where is a Sturm–Liouville operator or generator of a non-singular diffusion in an interval. This allows us to obtain the best constant in the L1-Poincaré inequality (a little stronger than the Cheeger isoperimetric inequality) and some sharp transportation–information inequalities and concentration inequalities for empirical means. We conclude with several illustrative...

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