  In this paper, we consider the boundedness of Rihaczek distributions acting
from Wiener amalgam spaces to modulation and Fourier modulation spaces. We give
several characterizations on different levels, and find that this type of
boundedness has the nature of self improvement. As applications, sharp
exponents are established for the boundedness in several typical cases.
Correspondingly, the boundedness of pseudodifferential operators on Wiener
amalgam spaces with symbols in modulation and Fourier modulation spaces are
also established. In some typical cases, we also find the full range of
exponents for the boundedness, including the recapture and essential extensions
of the main results in [IMRN, (10):1860-1893, (2010)] and [JFAA, 23(4):810-816,
(2017)].
