Bochner-Riesz Means and K-Functional on Triebel-Lizorkin Spaces

Based on n-dimensional Euclidean spaces and n-dimensional torus as underlying spaces, we investigate the rate for the norm convergence of the generalized Bochner-Riesz means on homogeneous Triebel-Lizorkin spaces, and establish the equivalence between the rate and the K-functional. Particularly, we show that such equivalence is closely related to the Bochner-Riesz conjecture on homogeneous Triebel-Lizorkin spaces. Thus, we obtain natural extensions of some well-known theorems by Fefferman, Tomas and Stein and by Carleson, Sojlin and Hormander.