Truncation in Besov-Morrey and Triebel-Lizorkin-Morrey spaces

Abstract

We will prove that under certain conditions on the parameters the operators $T^{+}f = \max(f,0)$ and $Tf = |f|$ are bounded mappings on the Triebel-Lizorkin-Morrey and Besov-Morrey spaces. Moreover we will show that some of the conditions we mentioned before are also necessary. Furthermore we prove that for