Counting metric spaces

If κ is a cardinal number, then any class of mutually non-homeomorphic metric spaces of size κ must be a set whose cardinality cannot exceed 2 ^κ . Our main result is a vivid construction of 2 ^κ mutually non-homeomorphic complete and both path connected and locally path connected metric spaces of size κ for each cardinal number κ from continuum up. Additionally we also deal with counting problems concerning countable metric spaces and Euclidean spaces.     

Sur un théorème de J. L. Krivine concernant la caracterisation des classes d’espaces isomorphes a des espaces d’orlicz généralisés et des classes voisines

The classL ^p the classes λ-SL ^p of spaces λ isomorphic to subspaces ofL ^p spaces and λ-QL ^p of subquotients have been characterized in the literature by formulas of certain simple forms. A theorem of Krivine gives a general demonstration of these results in the framework of ψ normed spaces. In particular, characterizations of subspaces and subquotients of certain classes of generalized Orlicz spaces are obtained.      

Hardy Spaces on ? n with Pointwise Variable Anisotropy

In this work we develop highly geometric Hardy spaces, for the full range 0<p≤1. These spaces are constructed over multi-level ellipsoid covers of ℝ ⁿ that are highly anisotropic in the sense that the ellipsoids can change shape rapidly from point to point and from level to level. This generalizes previous work on anisotropic Hardy spaces where the geometry of the space was ‘fixed’ over ℝ ⁿ and extends Hardy spaces over spaces of homogeneous type, where the theory holds for p values that are ‘close’ to 1.     

COEFFICIENT MULTIPLIERS ON MIXED NORM SPACES

§1　IntroductionSuppose thatf is analytic in the open unit disc D in the complex plane.We defineMp(r,f) =12π∫2π0 | f(reiθ) | pdθ1 / p,0

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On some new type generalized difference sequence spaces

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Sharp Estimates in Bergman and Besov Spaces on Bounded Symmetric Domains

Sharp estimates of the point-evaluation functional in weighted Bergman spaces L ^p _a (Ω, dν _α) and for the point-evaluation derivalive functional in Besov spaces B ^p (Ω) are obtained for bounded symmetric domains Ω in ℂ ⁿ . Received October 25, 1999, Accepted December 6, 2000     

Weak Morrey spaces and strong solutions to the Navier-Stokes equations

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Representation,interpolation, and reiteration theorems for generalized approximation spaces

We show that the representation theorem for classical approximation spaces can be generalized to spaces A(X,l ^q (ℬ))={f∈X:{E _n (f)}∈l ^q (ℬ)} in which the weighted l ^q -space l ^q (ℬ) can be (more or less) arbitrary. We use this theorem to show that generalized approximation spaces can be viewed as real interpolation spaces (defined with K-functionals or main-part K-functionals) between couples of quasi-normed spaces which satisfy certain Jackson and Bernstein-type inequalities. Especially, interpolation between an approximation space and the underlying quasi-normed space leads again to an approximation space. Together with a general reiteration theorem, which we also prove in the present paper, we obtain formulas for interpolation of two generalized approximation spaces. Received: December 6, 2001; in final form: April 2, 2002?Published online: March 14, 2003     

A substitute for the Sard-Smale theorem in theC 1 case

IfF is a Fredholm mapping of indexΝ ∃ ℤ and classC ^max(Ν,0)+1 between separable Banach spaces, the Sard—Smale theorem yields the existence of arbitrarily small perturbations ofF having 0 as a regular value. The smoothness requirement cannot be weakened in the Sard—Smale theorem itself, at least whenΝ ≥ 0, but we prove that the approximation result remains valid irrespective of the indexΝ whenF is only of classC ¹ and satisfies appropriate properness-like conditions. The separability of the spaces is not needed either. Everything carries over to the setting of Banach manifolds modeled on spaces with a norm of classC ¹ away from the origin. We also show that in Banach spaces, theC ¹ norm assumption can be dropped without major prejudice. The application to degree theory forC ¹ Fredholm mappings of index 0 is developed in a separate paper.     

Fixed points of asymptotically regular semigroups in Banach spaces

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Conical square function estimates in UMD Banach spaces and applications to H ∞-functional calculi

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Whitney’s jets for Sobolev functions

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Boundedness of commutators on Hardy type spaces

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Some consequences of Pisier’s approach to interpolation

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Spaces of functions of fractional smoothness on an irregular domain

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Hypersingular parameterized Marcinkiewicz integrals with variable kernels on Sobolev and Hardy-Sobolev spaces

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N-Widths and Average Widths of Besov Classes in Sobolev Spaces

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On banach spaces which containl 1(τ) and types of measures on compact spaces

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Isometries between Banach spaces of Lipschitz functions

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