Geodesic
Ball's lemma as an exercise
Čebyševskij sbornik, Tome 22 (2021) no. 3, pp. 464-466.

Voir la notice de l'article provenant de la source Math-Net.Ru

We suggest an extremely short proof of Ball's lemma by means of harmonic analysis only.
Keywords: Ball's lemma, Fourier transform, Hausdorff–Young inequality, Babenko–Beckner constant. 
@article{CHEB_2021_22_3_a30,
     author = {E. Liflyand},
     title = {Ball's lemma as an exercise},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {464--466},
     publisher = {mathdoc},
     volume = {22},
     number = {3},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2021_22_3_a30/}
}
TY  - JOUR
AU  - E. Liflyand
TI  - Ball's lemma as an exercise
JO  - Čebyševskij sbornik
PY  - 2021
SP  - 464
EP  - 466
VL  - 22
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CHEB_2021_22_3_a30/
LA  - en
ID  - CHEB_2021_22_3_a30
ER  - 
%0 Journal Article
%A E. Liflyand
%T Ball's lemma as an exercise
%J Čebyševskij sbornik
%D 2021
%P 464-466
%V 22
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CHEB_2021_22_3_a30/
%G en
%F CHEB_2021_22_3_a30
E. Liflyand. Ball's lemma as an exercise. Čebyševskij sbornik, Tome 22 (2021) no. 3, pp. 464-466. http://geodesic.mathdoc.fr/item/CHEB_2021_22_3_a30/

[1] K. I. Babenko, “An inequality in the theory of Fourier integral”, Izv. Akad. Nauk SSSR Ser. Mat., 25 (1961), 531–542 (Russian) | Zbl

[2] K. Ball, “Cube slicing in ${R}^n$”, Proc. Amer. Math. Soc., 97 (1986), 465–473 | MR | Zbl

[3] W. Beckner, “Inequalities in Fourier analysis”, Ann. Math., 102 (1975), 159–182 | DOI | MR | Zbl

[4] S. Bochner, Lectures on Fourier Integrals, Princeton Univ. Press, Princeton, N. J., 1959 | MR | Zbl

[5] B. Makarov, A. Podkorytov, Real Analysis: Measures, Integrals and Applications, Springer, 2013 | MR | Zbl