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Singular integral operators with non-smooth kernels on irregular domains.

Xuan Thinh Duong, Alan McIntosh (1999)

Revista Matemática Iberoamericana

Let χ be a space of homogeneous type. The aims of this paper are as follows.i) Assuming that T is a bounded linear operator on L2(χ), we give a sufficient condition on the kernel of T such that T is of weak type (1,1), hence bounded on Lp(χ) for 1 < p ≤ 2; our condition is weaker then the usual Hörmander integral condition.ii) Assuming that T is a bounded linear operator on L2(Ω) where Ω is a measurable subset of χ, we give a sufficient condition on the kernel of T so that T is of weak type...

SLE et invariance conforme

Jean Bertoin (2003/2004)

Séminaire Bourbaki

Les processus de Schramm-Loewner (SLE) induisent des courbes aléatoires du plan complexe, qui vérifient une propriété d’invariance conforme. Ce sont des outils fondamentaux pour la compréhension du comportement asymptotique en régime critique de certains modèles discrets intervenant en physique statistique ; ils ont permis notamment d’établir rigoureusement certaines conjectures importantes dans ce domaine.

Smooth operators for the regular representation on homogeneous spaces

Severino Melo (2000)

Studia Mathematica

A necessary and sufficient condition for a bounded operator on L 2 ( M ) , M a Riemannian compact homogeneous space, to be smooth under conjugation by the regular representation is given. It is shown that, if all formal ’Fourier multipliers with variable coefficients’ are bounded, then they are also smooth. In particular, they are smooth if M is a rank-one symmetric space.

Solutions analytiques des équations invariantes sur un groupe compact ou complexe réductif

André Cerezo (1975)

Annales de l'institut Fourier

Dans la première partie on caractérise les opérateurs différentiels invariants sur un groupe de Lie compact qui possèdent diverses propriétés de résolubilité analytiques : pour cela on développe en séries de Fourier les fonctions analytiques et les hyperfonctions sur le groupe.La deuxième partie est l’étude de la résolubilité des opérateurs invariants sur un groupe complexe réductif dans l’espace des fonctions holomorphes ; on développe celles-ci en série de “Laurent” suivant un sous-groupe compact...

Solvability of invariant sublaplacians on spheres and group contractions

Fulvio Ricci, Jérémie Unterberger (2001)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In the first part of this paper we study the local and global solvability and the hypoellipticity of a family of left-invariant sublaplacians L α on the spheres S 2 ⁢ n + 1 ≃ U ⁢ n + 1 / U ⁢ n . In the second part, we introduce a larger family of left-invariant sublaplacians L α , β on S 3 ≃ S ⁢ U ⁢ 2 and study the corresponding properties by means of a Lie group contraction to the Heisenberg group.

Solved and unsolved problems in generalized notions of amenability for Banach algebras

Yong Zhang (2010)

Banach Center Publications

We survey the recent investigations on approximate amenability/contractibility and pseudo-amenability/contractibility for Banach algebras. We will discuss the core problems concerning these notions and address the significance of any solutions to them to the development of the field. A few new results are also included.

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