On maximal operators on $k$-spheres in $\mathbb {Z}^{n}$
HTML articles powered by AMS MathViewer
- by Muharem Avdispahić and Lejla Smajlović PDF
- Proc. Amer. Math. Soc. 134 (2006), 2125-2130 Request permission
Abstract:
A. Magyar’s result on $L^{p}$-bounds for a family of operators on $k$-spheres ($k\geq 3$) in $\mathbb {Z}^{n}$ is improved to match the corresponding theorem for $2$-spheres.References
- A. H. Hardy and J. E. Littlewood, A new solution of Waring’s problem, Quart. J. Math. 48 (1919), 272-293.
- A. H. Hardy and S. Ramanujan, Asymptotic formula in combinatory analysis, Proc. London Math. Soc. Ser. 2, 17 (1918), 75-115.
- A. A. Karatsuba, Vinogradova otsenki, Matematicheskaya entsiklopediya, Vol. 1, Moscow, 1977.
- Akos Magyar, $L^p$-bounds for spherical maximal operators on $\mathbf Z^n$, Rev. Mat. Iberoamericana 13 (1997), no. 2, 307–317. MR 1617657, DOI 10.4171/RMI/222
- A. Magyar, E. M. Stein, and S. Wainger, Discrete analogues in harmonic analysis: spherical averages, Ann. of Math. (2) 155 (2002), no. 1, 189–208. MR 1888798, DOI 10.2307/3062154
- Melvyn B. Nathanson, Additive number theory, Graduate Texts in Mathematics, vol. 164, Springer-Verlag, New York, 1996. The classical bases. MR 1395371, DOI 10.1007/978-1-4757-3845-2
- S. B. Stečkin, An estimate of a complete rational trigonometric sum, Trudy Mat. Inst. Steklov. 143 (1977), 188–207, 211 (Russian). Analytic number theory, mathematical analysis and their applications (dedicated to I. M. Vinogradov on his 85th birthday). MR 0480376
- E. M. Stein, Maximal functions: Spherical means, Proc. Nat. Acad. Sci. USA 73 (1976), 2174-2175.
- I. M. Vinogradov, Metod trigonometricheskikh summ v teorii chisel, 2nd ed., “Nauka”, Moscow, 1980 (Russian). MR 603100
Additional Information
- Muharem Avdispahić
- Affiliation: Department of Mathematics, University of Sarajevo, Zmaja od Bosne 35, 71000 Sarajevo, Bosnia and Herzegovina
- MR Author ID: 28365
- ORCID: 0000-0001-7836-4988
- Email: mavdispa@pmf.unsa.ba
- Lejla Smajlović
- Affiliation: Department of Mathematics, University of Sarajevo, Zmaja od Bosne 35, 71000 Sarajevo, Bosnia and Herzegovina
- ORCID: 0000-0002-2709-5535
- Email: lejlas@pmf.unsa.ba
- Received by editor(s): February 21, 2005
- Published electronically: January 17, 2006
- Communicated by: Michael T. Lacey
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 134 (2006), 2125-2130
- MSC (2000): Primary 42B25, 11P55
- DOI: https://doi.org/10.1090/S0002-9939-06-08458-9
- MathSciNet review: 2215783