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The notion of an adapted coordinate system, introduced by V .I. Arnol’d, plays an important role in the study of asymptotic expansions of oscillatory integrals. In two dimensions, A. N. Varchenko gave sufficient conditions for the adaptness of a given coordinate system and proved the existence of an adapted coordinate system for a class of analytic… (More)

- Isroil A. Ikromov, Colin de Verdier
- 2007

We consider hypersurfaces S ⊂ IR with zero Gaussian curvature at every ordinary point with surface measure dS and define the surface measure dμ = ψ(x)dS(x) for smooth function ψ with compact support. We obtain uniform estimates for the Fourier transform of measures concentrated on such hypersurfaces. We show that due to the damping effect of the surface… (More)

We study the boundedness problem for maximal operatorsM associated to smooth hypersurfaces S in 3-dimensional Euclidean space. For p > 2, we prove that if no affine tangent plane to S passes through the origin and S is analytic, then the associated maximal operator is bounded on L(R) if and only if p > h(S), where h(S) denotes the so-called height of the… (More)

- Isroil A. Ikromov, Akhmadjon Soleev
- CASC
- 2006

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