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Besov spaces and function series on Lie groups

Leszek Skrzypczak (1993)

Commentationes Mathematicae Universitatis Carolinae

In the paper we investigate the absolute convergence in the sup-norm of Harish-Chandra's Fourier series of functions belonging to Besov spaces defined on non-compact connected Lie groups.

Besov spaces and function series on Lie groups (II).

Leszek Skrzypczak (1993)

Collectanea Mathematica

In this paper we investigate the absolute convergence in the sup-norm of two-sided Harish-Chandra's Fourier series of functions belonging to Zygmund-Hölder spaces defined on non-compact connected Lie groups.[Part I of the article in MR1240211].

Beurling-Figà-Talamanca-Herz algebras

Serap Öztop, Volker Runde, Nico Spronk (2012)

Studia Mathematica

For a locally compact group G and p ∈ (1,∞), we define and study the Beurling-Figà-Talamanca-Herz algebras A p ( G , ω ) . For p = 2 and abelian G, these are precisely the Beurling algebras on the dual group Ĝ. For p = 2 and compact G, our approach subsumes an earlier one by H. H. Lee and E. Samei. The key to our approach is not to define Beurling algebras through weights, i.e., possibly unbounded continuous functions, but rather through their inverses, which are bounded continuous functions. We prove that...

Closed convex hull of set of measurable functions, Riemann-measurable functions and measurability of translations

Michel Talagrand (1982)

Annales de l'institut Fourier

Let G be a locally compact group. Let L t be the left translation in L ∞ ( G ) , given by L t f ( x ) = f ( t x ) . We characterize (undre a mild set-theoretical hypothesis) the functions f ∈ L ∞ ( G ) such that the map t → L t f from G into L ∞ ( G ) is scalarly measurable (i.e. for φ ∈ L ∞ ( G ) * , t → φ ( L t f ) is measurable). We show that it is the case when t → θ ( L f t ) is measurable for each character θ , and if G is compact, if and only if f is Riemann-measurable. We show that t → L t f is Borel measurable if and only if f is left uniformly continuous.Some of the measure-theoretic tools used there...

Construction of Sobolev spaces of fractional order with sub-riemannian vector fields

Sami Mustapha, François Vigneron (2007)

Annales de l’institut Fourier

Given a smooth family of vector fields satisfying Chow-Hörmander’s condition of step 2 and a regularity assumption, we prove that the Sobolev spaces of fractional order constructed by the standard functional analysis can actually be “computed” with a simple formula involving the sub-riemannian distance.Our approach relies on a microlocal analysis of translation operators in an anisotropic context. It also involves classical estimates of the heat-kernel associated to the sub-elliptic Laplacian.

Currently displaying 41 – 60 of 285