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We study connections between the Boyd indices in Orlicz spaces and the growth conditions frequently met in various applications, for instance, in the regularity theory of variational integrals with non-standard growth. We develop a truncation method for computation of the indices and we also give characterizations of them in terms of the growth exponents and of the Jensen means. Applications concern variational integrals and extrapolation of integral operators.

Induced contraction semigroups and random ergodic theorems [Book]

T. Yoshimoto (1976)

Inductive and projective limits of $L_{p}$ spaces

Davis, Henry W., Murray, F.J., Weber, J.K. (1972)

Portugaliae mathematica

Inductive limit topologies on Orlicz spaces

Marian Nowak (1991)

Commentationes Mathematicae Universitatis Carolinae

Let $L^{ϕ}$ be an Orlicz space defined by a convex Orlicz function $ϕ$ and let $E^{ϕ}$ be the space of finite elements in $L^{ϕ}$ (= the ideal of all elements of order continuous norm). We show that the usual norm topology $𝒯_{ϕ}$ on $L^{ϕ}$ restricted to $E^{ϕ}$ can be obtained as an inductive limit topology with respect to some family of other Orlicz spaces. As an application we obtain a characterization of continuity of linear operators defined on $E^{ϕ}$ .

Inégalités de Sobolev-Orlicz non-uniformes

Gilles Carron (1998)

Colloquium Mathematicae

Inégalités isopérimétriques et inégalités de Faber-Krahn

Gilles Carron (1994/1995)

Séminaire de théorie spectrale et géométrie

Inégalités isopérimétriques et intégrales de Dirichlet gaussiennes

Antoine Ehrhard (1984)

Annales scientifiques de l'École Normale Supérieure

Inequalities for a regular polygon in $L^{p}$ spaces

M. Pavlović (1992)

Matematički Vesnik

Inequalities for Fourier transforms

Max Jodeit, Alberto Torchinsky (1971)

Studia Mathematica

Inequalities for Jacobians: interpolation techniques

Mario Milman (1993)

Revista colombiana de matematicas

Inequivalence of Wavelet Systems in $L ₁ (ℝ^{d})$ and $B V (ℝ^{d})$

Paweł Bechler (2005)

Bulletin of the Polish Academy of Sciences. Mathematics

Theorems stating sufficient conditions for the inequivalence of the d-variate Haar wavelet system and another wavelet system in the spaces $L ₁ (ℝ^{d})$ and $B V (ℝ^{d})$ are proved. These results are used to show that the Strömberg wavelet system and the system of continuous Daubechies wavelets with minimal supports are not equivalent to the Haar system in these spaces. A theorem stating that some systems of smooth Daubechies wavelets are not equivalent to the Haar system in $L ₁ (ℝ^{d})$ is also shown.

Infinite Dimensional Polytopes.

Ka-Sing Lau (1973)

Mathematica Scandinavica

Injections de Sobolev probabilistes et applications

Nicolas Burq, Gilles Lebeau (2013)

Annales scientifiques de l'École Normale Supérieure

On démontre dans cet article des versions probabilistes des injections de Sobolev sur une variété riemannienne compacte, $(M, g)$ . Plus précisément on démontre que pour des mesures de probabilité naturelles sur l’espace $L^{2} (M)$ , presque toute fonction appartient à tous les espaces $L^{p} (M)$ , $p < + \infty$ . On donne ensuite des applications à l’étude des harmoniques sphériques sur la sphère $𝕊^{d}$ : on démontre (encore pour des mesures de probabilité naturelles) que presque toute base hilbertienne de $L^{2} (𝕊^{d})$ formée d’harmoniques sphériques...

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Imbeddings between weighted Orlicz-Lorentz spaces.

In non-locally bounded $L_{φ}$ -spaces the norm is not almost transitive

Inclusions of Hardy-Orlicz spaces.

Indices for Banach Function Spaces.

Indices of Orlicz spaces and some applications