An equivalence theorem for a K-functional constructed by Beltrami–Laplace operator on symmetric spaces

The purpose of this article is to establish the equivalence between a K-functional and a spherical modulus of smoothness generated by Beltrami–Laplace operator Λ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Lambda $$\end{document} on noncompact rank 1 Riemannian symmetric spaces.