Calderón-Zygmund theory on trees and sparse domination for the radial Bergman projection

The purpose of this thesis is to provide new developments of some aspects of harmonic analysis on trees. The classical Calderón-Zygmund theory is adapted to this discrete setting in the doubling case, and a new general Calderón-Zygmund theory for non-locally doubling trees is introduced. Moreover, sparse domination techniques are exploited to investigate the Bergman projection, an operator of great relevance in the study of trees.