Unimodular multipliers on $alpha$-modulation spaces: A revisit with new method under weaker conditions

By a new method derived from Nicola--Primo--Tabacco[24], we study the boundedness on $alpha$-modulation spaces of unimodular multipliers with symbol $e^{imu(xi)}$. Comparing with the previous results, the boundedness result is established for a larger family of unimodular multipliers under weaker assumptions.