Extension of Variable Triebel-Lizorkin-Type Space on Domains

Let Omega subset of R-n (n >= 2) be a special Lipschitz domain. In this article, via the Peetre maximal function and following the approach of Rychkov who establish the extension results for the classical Triebel-Lizorkin spaces and Besov spaces, the authors show that the operator f bar right arrow Sigma(infinity)(j=0) psi(j) * (phi(j) * f)(Omega) is an extension from the variable Triebel-Lizorkin-type space on domain Omega, F-p(.),q(.)(s(.),phi) (Omega), to the corresponding space on R-n.

Automated summary

In this article, the authors demonstrate that the operator extending from the variable Triebel-Lizorkin-type space on domain Omega to the corresponding space on R-n via the Peetre maximal function and following the approach of Rychkov. This extension is based on the establishment of extension results for the classical Triebel-Lizorkin spaces and Besov spaces.