Affiliation:
1. Université Paris Cité and Sorbonne Université CNRS, IMJ‐PRG Paris France
2. Laboratory of Functional Analysis and Geometry of Spaces Faculty of Mathematics and Computer Science University of M'Sila M'Sila Algeria
Abstract
AbstractWe consider the composition operators acting on the real‐valued homogeneous Besov or Triebel–Lizorkin spaces, realized as dilation invariant subspaces of , denoted as . If and , then any function acting by composition on is necessarily linear. The above conditions are optimal: (i) in case , (Besov space), (Triebel–Lizorkin space), is a quasi‐Banach algebra for the pointwise product, (ii) in case , , , any function such that is a finite measure, and , acts by composition on .