Geodesic
Bellman vs Beurling: sharp estimates of uniform convexity for $L^p$ spaces
Algebra i analiz, Tome 27 (2015) no. 2, pp. 218-231.

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

@article{AA_2015_27_2_a8,
     author = {P. B. Zatitskiy and P. Ivanishvili and D. M. Stolyarov},
     title = {Bellman vs {Beurling:} sharp estimates of uniform convexity for $L^p$ spaces},
     journal = {Algebra i analiz},
     pages = {218--231},
     publisher = {mathdoc},
     volume = {27},
     number = {2},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AA_2015_27_2_a8/}
}
TY  - JOUR
AU  - P. B. Zatitskiy
AU  - P. Ivanishvili
AU  - D. M. Stolyarov
TI  - Bellman vs Beurling: sharp estimates of uniform convexity for $L^p$ spaces
JO  - Algebra i analiz
PY  - 2015
SP  - 218
EP  - 231
VL  - 27
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AA_2015_27_2_a8/
LA  - ru
ID  - AA_2015_27_2_a8
ER  - 
%0 Journal Article
%A P. B. Zatitskiy
%A P. Ivanishvili
%A D. M. Stolyarov
%T Bellman vs Beurling: sharp estimates of uniform convexity for $L^p$ spaces
%J Algebra i analiz
%D 2015
%P 218-231
%V 27
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AA_2015_27_2_a8/
%G ru
%F AA_2015_27_2_a8
P. B. Zatitskiy; P. Ivanishvili; D. M. Stolyarov. Bellman vs Beurling: sharp estimates of uniform convexity for $L^p$ spaces. Algebra i analiz, Tome 27 (2015) no. 2, pp. 218-231. http://geodesic.mathdoc.fr/item/AA_2015_27_2_a8/

[1] Ball K., Carlen E., Lieb E., “Sharp uniform convexity and smoothness inequlities for trace norms”, Invent. Math., 115:3 (1994), 463–482 | DOI | MR | Zbl

[2] Burkholder D. L., “Boundary value problems and sharp inequalities for martingale transforms”, Ann. Probab., 12:3 (1984), 647–702 | DOI | MR | Zbl

[3] Caffarelli L., Nirenberg L., Spruck J., “The Dirichlet problem for the degenerate Monge–Ampère equation”, Rev. Mat. Iberoamericana, 2:1–2 (1986), 19–27 | DOI | MR

[4] Clarkson J. A., “Uniformly convex spaces”, Trans. Amer. Math. Soc., 40:3 (1936), 396–414 | DOI | MR | Zbl

[5] Diestel J., Jarschow H., Tonge A., Absolutely summing operators, Cambridge Stud. Adv. Math., 43, Cambridge Univ. Press, Cambridge, 1995 | MR | Zbl

[6] Hanner O., “On the uniform convexity of $L^p$ and $l^p$”, Ark. Mat., 3 (1956), 239–244 | DOI | MR | Zbl

[7] Ivanishvili P., Osipov N. N., Stolyarov D. M., Vasyunin V. I., Zatitskiy P. B., “On Bellman function for extremal problems in BMO”, C. R. Math. Acad. Sci. Paris, 350:11–12 (2012), 561–564 | DOI | MR | Zbl

[8] Nazarov F., Treil S., Volberg A., “A Bellman function in stochastic control and harmonic analysis”, Oper. Theory Adv. Appl., 129, Birkhäuser, Basel, 2001, 393–423 | MR | Zbl

[9] Slavin L., Vasyunin V., “Sharp $L^p$ estimates on BMO”, Indiana Univ. Math. J., 61:3 (2012), 1051–1110 | DOI | MR | Zbl

[10] Vasyunin V. I., “Tochnye konstanty v obratnom neravenstve Gëldera dlya vesov Makenkhaupta”, Algebra i analiz, 15:1 (2003), 73–117 | MR | Zbl

[11] Ivanishvili P., Osipov N. N., Stolyarov D. M., Vasyunin V. I., Zatitskii P. B., Funktsiya Bellmana dlya ekstremalnykh zadach v prostranstve BMO, Preprint No 19, POMI, 2011; arXiv: ; Trans. Amer. Math. Soc. (to appear) 1205.7018

[12] Pogorelov A. I., Differentsialnaya geometriya, 6-e izd., Nauka, M., 1974 | MR