Geodesic
Damped Oscillatory Integrals and Maximal Operators
Matematičeskie zametki, Tome 78 (2005) no. 6, pp. 833-852

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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. 
@article{MZM_2005_78_6_a3,
     author = {I. A. Ikromov},
     title = {Damped {Oscillatory} {Integrals} and {Maximal} {Operators}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {833--852},
     publisher = {mathdoc},
     volume = {78},
     number = {6},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2005_78_6_a3/}
}
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I. A. Ikromov. Damped Oscillatory Integrals and Maximal Operators. Matematičeskie zametki, Tome 78 (2005) no. 6, pp. 833-852. http://geodesic.mathdoc.fr/item/MZM_2005_78_6_a3/