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Uniform G-Convexity for Vector-Valued Lp Spaces

Boyko, Nataliia, Kadets, Vladimir (2009)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 46B20.Uniform G-convexity of Banach spaces is a recently introduced natural generalization of uniform convexity and of complex uniform convexity. We study conditions under which uniform G-convexity of X passes to the space of X-valued functions Lp (m,X).

Uniformly μ -continuous topologies on Köthe-Bochner spaces and Orlicz-Bochner spaces

Krzysztof Feledziak (1998)

Commentationes Mathematicae Universitatis Carolinae

Some class of locally solid topologies (called uniformly μ -continuous) on Köthe-Bochner spaces that are continuous with respect to some natural two-norm convergence are introduced and studied. A characterization of uniformly μ -continuous topologies in terms of some family of pseudonorms is given. The finest uniformly μ -continuous topology 𝒯 I ϕ ( X ) on the Orlicz-Bochner space L ϕ ( X ) is a generalized mixed topology in the sense of P. Turpin (see [11, Chapter I]).

Unions et intersections d’espaces L p invariantes par translation ou convolution

Jean-Paul Bertrandias, Christian Datry, Christian Dupuis (1978)

Annales de l'institut Fourier

Étude des propriétés des unions et intersections d’espaces L p ( s ) relatifs à un ensemble S de mesures positives sur un groupe commutatif localement compact lorsque S est invariant par translation ou stable par convolution.Dans des cas particuliers, on retrouve les propriétés d’espaces étudiés par A. Beurling et par B. Koremblium.On étudie aussi les espaces p ( L p ' ) formés des fonctions appartenant localement à L p ' et qui ont un comportement p à l’infini.

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