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 $p<u$ in many cases the Triebel-Lizorkin-Morrey spaces do not have the Fubini property.

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