Uniform estimates for oscillatory integrals with homogeneous polynomial phases of degree 4

  title={Uniform estimates for oscillatory integrals with homogeneous polynomial phases of degree 4},
  author={Michael Ruzhansky and A. R. Safarov and G. A. Khasanov},
  journal={Analysis and Mathematical Physics},
In this paper we consider the uniform estimates for oscillatory integrals with homogeneous polynomial phases of degree 4 in two variables. The obtained estimate is sharp and the result is an analogue of the more general theorem of Karpushkin (Proc I.G.Petrovsky Seminar 9:3–39, 1983) for sufficiently smooth functions, thus, in particular, removing the analyticity assumption. 



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