Heat Semi-Group and Function Spaces on Symmetric Spaces of Non-Compact Type

Abstract

Besov-Triebel scales of function spaces defined on symmetric spaces of non-compact type are investigated. We prove an atomic decomposition theorem for the function spaces and give their characterization in terms of heat semigroup. In consequence we can describe the spectrum of the Laplace-Beltrami operator in these spaces and improve the generalized Riemann-Lebesgue lemma for the spherical Fourier transform.