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Uniform bounds for the bilinear Hilbert transforms (II).

Xiaochun Li (2006)

Revista Matemática Iberoamericana

We continue the investigation initiated in [Grafakos, L. and Li, X.: Uniform bounds for the bilinear Hilbert transforms (I). Ann. of Math. (2)159 (2004), 889-933] of uniform Lp bounds for the family of bilinear Hilbert transformsHα,β(f,g)(x) = p.v. ∫R f(x - αt) g (x - βt) dt/t.

Uniform Eberlein Compacta and Uniformly Gâteaux Smooth Norms

Fabian, Marián, Hájek, Petr, Zizler, Václav (1997)

Serdica Mathematical Journal

* Supported by grants: AV ĈR 101-95-02, GAĈR 201-94-0069 (Czech Republic) and NSERC 7926 (Canada).It is shown that the dual unit ball BX∗ of a Banach space X∗ in its weak star topology is a uniform Eberlein compact if and only if X admits a uniformly Gâteaux smooth norm and X is a subspace of a weakly compactly generated space. The bidual unit ball BX∗∗ of a Banach space X∗∗ in its weak star topology is a uniform Eberlein compact if and only if X admits a weakly uniformly rotund norm. In this case...

Uniform factorization for compact sets of weakly compact operators

Kristel Mikkor, Eve Oja (2006)

Studia Mathematica

We prove uniform factorization results that describe the factorization of compact sets of compact and weakly compact operators via Hölder continuous homeomorphisms having Lipschitz continuous inverses. This yields, in particular, quantitative strengthenings of results of Graves and Ruess on the factorization through p -spaces and of Aron, Lindström, Ruess, and Ryan on the factorization through universal spaces of Figiel and Johnson. Our method is based on the isometric version of the Davis-Figiel-Johnson-Pełczyński...

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).

Uniform maps into normed spaces

Zdeněk Frolìk (1974)

Annales de l'institut Fourier

Thirteen properties of uniform spaces are shown to be equivalent. The most important properties seem to be those related to modules of uniformly continuous mappings into normed spaces, and to partitions of unity.

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