  This work is concerned with the study of the adaptivity properties of
nonparametric regression estimators over the $d$-dimensional sphere within the
global thresholding framework. The estimators are constructed by means of a
form of spherical wavelets, the so-called needlets, which enjoy strong
concentration properties in both harmonic and real domains. The author
establishes the convergence rates of the $L^p$-risks of these estimators,
focussing on their minimax properties and proving their optimality over a scale
of nonparametric regularity function spaces, namely, the Besov spaces.
