Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

Request Permissions   Purchase Content 


An asymptotically sharp form of Ball's integral inequality

Authors: Ron Kerman, Rastislav Ol’hava and Susanna Spektor
Journal: Proc. Amer. Math. Soc. 143 (2015), 3839-3846
MSC (2010): Primary 33F05; Secondary 42A99
Published electronically: May 22, 2015
MathSciNet review: 3359575
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We solve the open problem of determining the second order term in the asymptotic expansion of the integral in Ball's integral inequality. In fact, we provide a method by which one can compute any term in the expansion. We also indicate how to derive an asymptotically sharp form of a generalized Ball's integral inequality.

References [Enhancements On Off] (What's this?)

  • [1] Keith Ball, Cube slicing in $ {\bf R}^n$, Proc. Amer. Math. Soc. 97 (1986), no. 3, 465-473. MR 840631 (87g:60018),
  • [2] David Borwein, Jonathan M. Borwein, and Isaac E. Leonard, $ L_p$ norms and the sinc function, Amer. Math. Monthly 117 (2010), no. 6, 528-539. MR 2662705 (2011d:26003),
  • [3] R. Kerman and S. Spektor, A new proof of the asymptotic limit of the $ L_p$ norm of the Sinc function, arXiv:1208.3799v1.
  • [4] H. König and A. Koldobsky, On the maximal measure of sections of the $ n$-cube, Proc. Southeast Geometry Seminar, Contemp. Math., 599, Amer. Math. Soc., Providence, RI, 2013. MR 3202477
  • [5] L. J. Landau, Bessel functions: monotonicity and bounds, J. London Math. Soc. (2) 61 (2000), no. 1, 197-215. MR 1745392 (2001a:33005),
  • [6] Fedor L. Nazarov and Anatoliy N. Podkorytov, Ball, Haagerup, and distribution functions, Complex analysis, operators, and related topics, Oper. Theory Adv. Appl., vol. 113, Birkhäuser, Basel, 2000, pp. 247-267. MR 1771767 (2001i:26022)
  • [7] Krzysztof Oleszkiewicz and Aleksander Pełczyński, Polydisc slicing in $ {\bf C}^n$, Studia Math. 142 (2000), no. 3, 281-294. MR 1792611 (2001f:52014)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 33F05, 42A99

Retrieve articles in all journals with MSC (2010): 33F05, 42A99

Additional Information

Ron Kerman
Affiliation: Department of Mathematics, Brock University, St. Catharines, Ontario, L2S 3A1, Canada

Rastislav Ol’hava
Affiliation: Department of Mathematics, Charles University, Sokolovska 83, Prague, Czech Republic

Susanna Spektor
Affiliation: Department of Mathematics, University of Alberta, Edmonton, Alberta, T6G 2G1, Canada

Keywords: Ball's integral inequality, Sinc function, asymptotic expansion, Bessel function
Received by editor(s): July 15, 2013
Received by editor(s) in revised form: March 3, 2014
Published electronically: May 22, 2015
Additional Notes: The research of the second author was supported by grant No. P201-13-14743S of the Grant Agency of the Czech Republic and by the grant SVV-2013-267316.
Communicated by: Walter Van Assche
Article copyright: © Copyright 2015 American Mathematical Society

American Mathematical Society