Truncation in Besov–Morrey and Triebel–Lizorkin–Morrey spaces. (March 2021) - Hovemann, Marc
Abstract: We will prove that under certain conditions on the parameters the operators T + f = max ( f, 0 ) and T f = | 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 in many cases the Triebel–Lizorkin–Morrey spaces do not have the Fubini property. Highlights: Truncation operator is bounded for Triebel–Lizorkin–Morrey spaces. Triebel–Lizorkin–Morrey spaces often have no Fubini property. Compared to Triebel–Lizorkin spaces new phenomenon appears.