Abstract: A hot topic in harmonic analysis is to study the boundedness of singular integral operators along submanifolds in various spaces. In this paper, we mainly used oscillatory integral estimation method and Fourier transform estimation method to extend the oscillatory integral operator along homogeneous curves to the oscillatory integral operator along a general curve satisfying certain conditions, and obtained the boundedness of the operator in the modulation space. Thus, some results of predecessors are generalized.

Key words: modulation space, Wiener amalgam spaces, oscillatory integral, curves, product domain