COMPOSITION OPERATORS on WIENER AMALGAM SPACES

Abstract

For a complex function F on C, we study the associated composition operator TF (f):= F-f = F (f) on Wiener amalgam W p;q(Rd) (1 6 p < 1; 1 6 q < 2). We have shown TF maps W p;1(Rd) to W p;q(Rd) if and only if F is real analytic on R2 and F (0) = 0. Similar result is proved in the case of modulation spaces Mp;q(Rd). In particular, this gives an affirmative answer to the open question proposed in Bhimani and Ratnakumar (J. Funct. Anal. 270(2) (2016), 621{648).