Geodesic
Integrability of the Fourier Transforms of Measures Concentrated on Hypersurfaces
Funkcionalʹnyj analiz i ego priloženiâ, Tome 49 (2015) no. 3, pp. 74-79

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This paper considers estimates for the Fourier transforms of signed measures concentrated on families of hypersurfaces. A theorem about the integrability of Randol-type maximal functions related to a certain class of nonconvex hypersurfaces is presented. The results are applied to study the integrability of the Fourier transforms of signed measures concentrated on certain hypersurfaces. In a special case, the exact integrability exponent of the Fourier transforms of measures is specified. The results improve a recent theorem of L. Erdős and M. Salmhofer.
Keywords: asymptotics, Fourier transforms, integrability, curvature. 
@article{FAA_2015_49_3_a7,
     author = {I. A. Ikromov},
     title = {Integrability of the {Fourier} {Transforms} of {Measures} {Concentrated} on {Hypersurfaces}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {74--79},
     publisher = {mathdoc},
     volume = {49},
     number = {3},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2015_49_3_a7/}
}
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I. A. Ikromov. Integrability of the Fourier Transforms of Measures Concentrated on Hypersurfaces. Funkcionalʹnyj analiz i ego priloženiâ, Tome 49 (2015) no. 3, pp. 74-79. http://geodesic.mathdoc.fr/item/FAA_2015_49_3_a7/