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Transference for hypergroups.

Giacomo Gigante (2001)

Collectanea Mathematica

A transference theorem for convolution operators is proved for certain families of one-dimensional hypergroups.

Transformation de Poisson sur un arbre localement fini

Ferdaous Kellil, Guy Rousseau (2005)

Annales mathématiques Blaise Pascal

Dans cet article on étudie en premier lieu la résolvante (le noyau de Green) d’un opérateur agissant sur un arbre localement fini. Ce noyau est supposé invariant par un groupe G d’automorphismes de l’arbre. On donne l’expression générique de cette résolvante et on établit des simplifications sous différentes hypothèses sur G .En second lieu on introduit la transformation de Poisson qui associe à une mesure additive finie sur l’espace Ω des bouts de l’arbre une fonction propre de l’ opérateur. On...

Translation-invariant operators on Lorentz spaces L(1,q) with 0 < q < 1

Leonardo Colzani, Peter Sjögren (1999)

Studia Mathematica

We study convolution operators bounded on the non-normable Lorentz spaces L 1 , q of the real line and the torus. Here 0 < q < 1. On the real line, such an operator is given by convolution with a discrete measure, but on the torus a convolutor can also be an integrable function. We then give some necessary and some sufficient conditions for a measure or a function to be a convolutor on L 1 , q . In particular, when the positions of the atoms of a discrete measure are linearly independent over the rationals,...

Two problems of Calderón-Zygmund theory on product-spaces

Jean-Lin Journé (1988)

Annales de l'institut Fourier

R. Fefferman has shown that, on a product-space with two factors, an operator T bounded on L 2 maps L into BMO of the product if the mean oscillation on a rectangle R of the image of a bounded function supported out of a multiple R’ of R, is dominated by C | R | s | R | - s , for some s &gt; 0 . We show that this result does not extend in general to the case where E has three or more factors but remains true in this case if in addition T is a convolution operator, provided s &gt; s 0 ( E ) . We also show that the Calderon-Coifman bicommutators,...

Two-weight Sobolev-Poincaré inequalities and Harnack inequality for a class of degenerate elliptic operators

Bruno Franchi, Cristian E. Gutiérrez, Richard L. Wheeden (1994)

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

In this Note we prove a two-weight Sobolev-Poincaré inequality for the function spaces associated with a Grushin type operator. Conditions on the weights are formulated in terms of a strong A weight with respect to the metric associated with the operator. Roughly speaking, the strong A condition provides relationships between line and solid integrals of the weight. Then, this result is applied in order to prove Harnack's inequality for positive weak solutions of some degenerate elliptic equations....

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.

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