COMPOSITION OPERATORS ON WIENER AMALGAM SPACES

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