Seminario Análisis y aplicaciones

Día y hora: Viernes 5 de Abril 2014, 11:30-12:30
Lugar: Aula 420, Módulo 17
Título: Boundedness of integral operators and sparse domination of Bergman projectors on trees
Resumen: Motivated by the connections existing between a homogeneous tree and the hyperbolic disk, one can see the tree hanged on a point at infinity as a discrete counterpart of the upper half plane. Together with F. De Mari and M. Monti, we consider a family of horocyclic measures that give rise to harmonic Bergman spaces, for which we explicitly compute some orthonormal bases and the kernels. We also establish boundedness results for integral operators, in particular for the Bergman projectors.

In an ongoing project with J. Conde Alonso, F. De Mari, M. Monti and M. Vallarino, we look at general radial trees and broaden the previous work. We assume the number of neighbors of a vertex to be bounded by 2 from below, but we allow it to be unbounded from above, leading to a non doubling setting. By considering a suitable family of dyadic sets, a non doubling Calderón-Zygmund decomposition and an extra condition on the size of the kernel, we obtain classical boundedness results for integral operators. Furthermore, assuming the tree to have bounded geometry, we prove sparse domination for the Bergman projectors. This implies in a different way the boundedness results, but also gives weighted estimates.

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