$L^p$-boundedness of pseudo-differential operators on homogeneous trees

Abstract

. The aim of this article is to study the L p -boundedness of pseudo-differen-tial operators on a homogeneous tree X . For p ∈ (1 , 2) , we establish a connection between the L p -boundedness of the pseudo-differential operators on X and that on the group of integers Z . We also prove an analogue of the Calderón–Vaillancourt theorem in the setting of homogeneous trees for p ∈ (1 , ∞ ) \ { 2 } .