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A new of looking at distributional estimates; applications for the bilinear Hilbert transform.

Dimitriy Bilyk, Loukas Grafakos (2006)

Collectanea Mathematica

Distributional estimates for the Carleson operator acting on characteristic functions of measurable sets of finite measure were obtained by Hunt. In this article we describe a simple method that yields such estimates for general operators acting on one or more functions. As an application we discuss how distributional estimates are obtained for the linear and bilinear Hilbert transform. These distributional estimates show that the square root of the bilinear Hilbert transform is exponentially lntegrable...

A sheaf of Boehmians

Jonathan Beardsley, Piotr Mikusiński (2013)

Annales Polonici Mathematici

We show that Boehmians defined over open sets of ℝⁿ constitute a sheaf. In particular, it is shown that such Boehmians satisfy the gluing property of sheaves over topological spaces.

A spectral analysis of automorphic distributions and Poisson summation formulas

André Unterberger (2004)

Annales de l’institut Fourier

Automorphic distributions are distributions on d , invariant under the linear action of the group S L ( d , ) . Combs are characterized by the additional requirement of being measures supported in d : their decomposition into homogeneous components involves the family ( 𝔈 i λ d ) λ , of Eisenstein distributions, and the coefficients of the decomposition are given as Dirichlet series 𝒟 ( s ) . Functional equations of the usual (Hecke) kind relative to 𝒟 ( s ) turn out to be equivalent to the invariance of the comb under some modification...

Décomposition microlocale analytique des distributions

G. Bengel, Pierre Schapira (1979)

Annales de l'institut Fourier

Nous dirons qu’un faisceau de groupes abéliens sur un espace topologique X est souple si, Ω étant un ouvert de X , F 1 et F 2 des fermés de Ω , toute section de sur Ω à support dans F 1 F 2 est somme de sections à support dans F 1 et F 2 . Soit M une variété analytique réelle, S * M son fibré cotangent en sphères, C f le faisceau sur S * M des microfonctions qui proviennent localement sur S * M , de distributions. Nous montrons que le faisceau C f est souple. En particulier le faisceau 𝒟 ' / 𝒜 sur M , quotient des distributions par...

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