Abstract We discuss the problem of estimating oscillatory integrals with a smooth phase function. A general result is presented on estimating these integrals using non-oscillatory intervals of a linear differential operator.We then derive a generalization of the Björk-type estimates and show how it can be used to estimate the integral by using lower bounds for the sum of derivatives of the phase function. Finally, we provide examples to illustrate the importance of the conditions under which these results apply to the bounds of oscillatory integrals.
Икромов et al. (Sun,) studied this question.
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