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

Characterization of boundedness on Wiener amalgam spaces of multilinear Rihaczek distributions