Localization property of generalized Besov-type spaces, Triebel-Lizorkin-type spaces and of their associated multiplier spaces

Abstract

In this paper, we study the localization property of generalized Besov-type spaces, Triebel-Lizorkin-type spaces and of their associated multiplier spaces, defineds from function $v:\ \left[ 0,\infty \right)\rightarrow ]0,\infty )$ satisfying the inequality $v(ts)\geq c\,t^{-\mu}v(s)$ for $0<t,s\leq 1$ and some real $\mu$.