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A transference theorem for convolution operators is proved for certain families of one-dimensional hypergroups.
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 d’automorphismes de l’arbre. On donne l’expression générique de cette résolvante et on établit des simplifications sous différentes hypothèses sur .En second lieu on introduit la transformation de Poisson qui associe à une mesure additive finie sur l’espace des bouts de l’arbre une fonction propre de l’ opérateur. On...
We study convolution operators bounded on the non-normable Lorentz spaces 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 . In particular, when the positions of the atoms of a discrete measure are linearly independent over the rationals,...
R. Fefferman has shown that, on a product-space with two factors, an operator T bounded on maps 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 , for some . 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 . We also show that the Calderon-Coifman bicommutators,...
We give some explicit values of the constants and in the inequality where denotes the norm of the Bergman projection on the space.
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 weight with respect to the metric associated with the operator. Roughly speaking, the strong 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....
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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