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 
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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/

[1] Stein E.M., “Maximal functions: I. Spherical means”, Proc. Nat. Acad. Sci. U.S.A., 73:7 (1976), 2174–2175 | DOI | MR | Zbl

[2] Bourgain J., “Averages in the plane convex cuves and maximal operators”, J. Anal. Math., 47 (1986), 69–85 | DOI | MR | Zbl

[3] Simon L., Lectures on geometric measure theory, Proc. Centre Math. Anal., Austral. Nat. Univ., 3, Australian National University, Centre for Mathematical Analysis, Canberra, 1983 | Zbl

[4] Iosevich A., Sawyer E., “Maximal averages over surfaces”, Adv. Math., 132:1 (1997), 46–119 | DOI | MR | Zbl

[5] Iosevich A., Sawyer E., “Oscillatory integrals and maximal averages over homogeneous surfaces”, Duke Math. J., 82:1 (1996), 103–131 | DOI | MR

[6] Ikromov I.A., Kempe M., Müller D., “Estimates for maximal functions assosiated to hypersurfaces in $R^3$ and related problems of harmonic analysis”, Acta Math., 204 (2010), 151–271 | DOI | MR | Zbl

[7] Varchenko A.N., “Mnogogranniki Nyutona i otsenki ostsilliruyuschikh integralov”, Funkts. analiz i ego pril., 10:3 (1976), 13–38 | MR

[8] Sogge C.D., “Maximal operators associated to hypersurfaces with one nonvanishing principal curvature”, Fourier Anal. and Partial Diff. Equat. (Miraflores de la Sierra, 1992), Stud. Adv. Math., CRC, Boca Raton, FL, 1995, 317–323 | MR | Zbl

[9] Ikromov I.A., Usmanov S.E., “Ob ogranichennosti maksimalnykh operatorov, svyazannykh s giperpoverkhnostyami”, Sovremen. matem. Fundament. napravl., 64, no. 4, 2018, 650–681

[10] Schulz H., “Convex hypersurfaces of finite type and the asymptotics of their Fourier transforms”, Indiana Univ. Math. J., 40:4 (1991), 1267–1275 | DOI | MR | Zbl

[11] Ikromov I.A., Müller D., Fourier restriction for hypersurfaces in three dimensions and Newton polyhedra, Princeton Univ. Press, 2016 | MR | Zbl

[12] Greenleaf A., “Principal curvature and harmonic analysis”, Indiana Math. J., 30:4 (1981), 519–537 | DOI | MR

[13] Sogge C.D., Stein E.M., “Averages of functions over hypersurfaces in $R^{n}$”, Invent. Math., 82:3 (1985), 543–556 | DOI | MR | Zbl

[14] Bruna J., Nagel A., and Wainger S., “Convex hypersurfaces and Fourier transforms”, Ann. Math., 127:2 (1988), 333–365 | DOI | MR | Zbl