Annals of Functional Analysis

On generalized Beckner's inequality

Kichi-Suke Saito and Ryotaro Tanaka

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

In this paper, we present generalizations of Beckner's inequality by using symmetric absolute normalized norms on $\mathbb{R}^2$.

Article information

Source
Ann. Funct. Anal., Volume 6, Number 1 (2015), 267-278.

Dates
First available in Project Euclid: 19 December 2014

Permanent link to this document
https://projecteuclid.org/euclid.afa/1419001465

Digital Object Identifier
doi:10.15352/afa/06-1-20

Mathematical Reviews number (MathSciNet)
MR3297802

Zentralblatt MATH identifier
1330.46020

Subjects
Primary: 46B20
Secondary: 46B99: None of the above, but in this section

Keywords
Beckner's inequality symmetric absolute normalized norm norm inequality

Citation

Saito, Kichi-Suke; Tanaka, Ryotaro. On generalized Beckner's inequality. Ann. Funct. Anal. 6 (2015), no. 1, 267--278. doi:10.15352/afa/06-1-20. https://projecteuclid.org/euclid.afa/1419001465


Export citation

References

  • W. Beckner, Inequalities in Fourier analysis, Ann. of Math. 102 (1975), 159–182.
  • R. Bhatia, Matrix analysis, Springer-Verlag, New York, 1997.
  • F.F. Bonsall and J. Duncan, Numerical ranges II, Cambridge University Press, Cambridge, 1973.
  • K.-I. Mitani, S. Oshiro and K.-S. Saito, Smoothness of $\psi$-direct sums of Banach spaces, Math. Inequal. Appl. 8 (2005), 147–157.
  • K.-I. Mitani, K.-S. Saito and T. Suzuki, Smoothness of absolute norms on $\mathbb{C}^n$, J. Convex Anal. 10 (2003), 89–107.
  • K.-S. Saito, M. Kato and Y. Takahashi, Von Neumann-Jordan constant of absolute normalized norms on $\mathbb{C}^2$, J. Math. Anal. Appl. 244 (2000), 515–532.
  • K.-S. Saito, M. Kato and Y. Takahashi, Absolute norms on $\mathbb{C}^n$, J. Math. Anal. Appl. 252 (2000), 879–905.
  • Y. Takahashi, M. Kato and K.-S. Saito, Strict convexity of absolute norms on $\mathbb{C}^2$ and direct sums of Banach spaces, J. Inequal. Appl. 7 (2002), 179–186.
  • R. Tanaka, K.-S. Saito and N. Komuro, Another approach to Beckner's inequality, J. Math. Inequal. 7 (2013), 543–549.