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Damped Oscillatory Integrals and Maximal Operators

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Abstract

In the present paper, we consider estimates of the Fourier transform of Borel measures concentrated on analytic hypersurfaces and containing a mitigating factor. The mitigating factors are expressed in terms of principal curvatures of the surface. The resulting estimates are applied to investigating the boundedness of the corresponding maximal operators.

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Authors and Affiliations

  1. Samarkand State University, Samarkand, Uzbekistan

    I. A. Ikromov

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  1. I. A. Ikromov
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__________

Translated from Matematicheskie Zametki, vol. 78, no. 6, 2005, pp. 833–852.

Original Russian Text Copyright ©2005 by I. A. Ikromov.

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Ikromov, I.A. Damped Oscillatory Integrals and Maximal Operators. Math Notes 78, 773–790 (2005). https://doi.org/10.1007/s11006-005-0183-z

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  • DOI: https://doi.org/10.1007/s11006-005-0183-z

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