$L^p$-boundedness of pseudo-differential operators on homogeneous trees
Volume 272 / 2023
Studia Mathematica 272 (2023), 221-244
MSC: Primary 58J40; Secondary 47G30, 43A85, 39A12, 20E08.
DOI: 10.4064/sm220816-27-3
Published online: 5 June 2023
Abstract
The aim of this article is to study the $L^p$-boundedness of pseudo-differential operators on a homogeneous tree $ \mathfrak X $. For $p\in (1,2)$, we establish a connection between the $L^{p}$-boundedness of the pseudo-differential operators on $ \mathfrak X $ and that on the group of integers $\mathbb Z$. We also prove an analogue of the Calderón–Vaillancourt theorem in the setting of homogeneous trees for $p\in (1,\infty )\setminus \{2\}$.
