Geodesic
On estimates for maximal operators
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2023), pp. 23-33

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The paper deals with boundedness problem for maximal operators associated to hypersurfaces in the space of integrable functions with degree p. A necessary condition for boundedness is given in the space of square-integrable functions in the case one nonvanishing principal curvature. A criterion for the boundedness of the maximal operators in the space of square-integrable functions is obtained for a partial class of convex hypersurfaces.
Keywords: maximal operator, boundedness.
Mots-clés : Fourier transform, hypersurface 
@article{IVM_2023_7_a2,
     author = {I. A. Ikromov and A. M. Barakayev},
     title = {On estimates for maximal operators},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {23--33},
     publisher = {mathdoc},
     number = {7},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2023_7_a2/}
}
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I. A. Ikromov; A. M. Barakayev. On estimates for maximal operators. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2023), pp. 23-33. http://geodesic.mathdoc.fr/item/IVM_2023_7_a2/