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We use broad-narrow method to estabish the sharp $L^4$ decay estimate for aclass of degenerate oscillatory integral operators in $(2+1)$ dimensions.Especially, the model phase function is  \[xt^2+y^2t,\] a cubic homogeneous polynomial which is degenerate in thesense of [28].

A sharp decay estimate for degnerate oscillatory integral operators using broad-narrow method