Estimates of fundamental solution for Kohn Laplacian in Besov and Triebel-Lizorkin spaces

Abstract

ABSTRACT We introduce Besov space B ˙ p α , q ( ∂ Ω k ) and Triebel-Lizorkin space F ˙ p α , q ( ∂ Ω k ) on a family of model domains ∂ Ω k = { ( z , z n + 1 ) = ( z 1 , z 2 , … , z n + 1 ) : Im ( z n + 1 ) = ϕ ( | z | 2 ) } with ϕ ( x ) = x k in C n + 1 which can be considered as a space of homogeneous type in the sense of Coifman RR, Weiss G.[Analyse Harmonique Non-commutative and Certains Espaces Homogǹes. Berlin: Springer; 1971. (Lecture Notes in Math.; 242).], Coifman R, Weiss G. [Extensions of Hardy spaces and their use in analysis. Bull Amer Math Soc. 1977;83:569–645.]. We study the sharp estimates on the fundamental solution for the Kohn Laplacian and Cauchy-Szegö projection on ∂ Ω k in these spaces.