Bellman approach to some problems in harmonic analysis
Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2001-2002), Exposé no. 19, 14 p.

The stochastic optimal control uses the differential equation of Bellman and its solution - the Bellman function. Recently the Bellman function proved to be an efficient tool for solving some (sometimes old) problems in harmonic analysis.

@article{SEDP_2001-2002____A19_0,
     author = {Volberg, Alexander},
     title = {Bellman approach to some  problems in harmonic analysis},
     journal = {S\'eminaire \'Equations aux d\'eriv\'ees partielles (Polytechnique) dit aussi "S\'eminaire Goulaouic-Schwartz"},
     note = {talk:19},
     publisher = {Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
     year = {2001-2002},
     language = {en},
     url = {http://www.numdam.org/item/SEDP_2001-2002____A19_0/}
}
TY  - JOUR
AU  - Volberg, Alexander
TI  - Bellman approach to some  problems in harmonic analysis
JO  - Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz"
N1  - talk:19
PY  - 2001-2002
DA  - 2001-2002///
PB  - Centre de mathématiques Laurent Schwartz, École polytechnique
UR  - http://www.numdam.org/item/SEDP_2001-2002____A19_0/
LA  - en
ID  - SEDP_2001-2002____A19_0
ER  - 
Volberg, Alexander. Bellman approach to some  problems in harmonic analysis. Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2001-2002), Exposé no. 19, 14 p. http://www.numdam.org/item/SEDP_2001-2002____A19_0/

[1] St. Buckley, Summation conditions on weights, Mich. Math. J. 40 (1993), 153-170. | MR 1214060 | Zbl 0794.42011

[2] R. Fefferman, C. Kenig, J. Pipher, The theory of weights and the Dirichlet problem for elliptic equations, Annals of Math, 134 (1991), 65-124. | MR 1114608 | Zbl 0770.35014

[3] D.L. Burkholder, Boundary value problems and sharp inequalities for martingale transforms, Annals of Prob. 12 (1984), 647-702. | MR 744226 | Zbl 0556.60021

[4] F. Nazarov, A. Volberg, Heating of the Ahlfors-Beurling operator and estimates of its norms, Preprint. | Zbl 1061.47042

[5] St. Petermichl, A. Volberg, Heating of the Ahlfors-Beurling operator : weakly quasiregular maps on the plane are quasiregular, To appear in Duke Math J. | MR 1894362 | Zbl 1025.30018

[6] F. Nazarov, S. Treil, A. Volberg, The Bellman functions and two-weight inequalities for Haar multipliers, J. of the Amer. Math. Soc., 12 (1999), N 4, 909-928. | MR 1685781 | Zbl 0951.42007

[7] F. Nazarov, S. Treil, The hunt for the Bellman function : applications to estimates of singular integral operators and to other classical problems in harmonic analysis, St Petersburg Math. J., 8 (1997), N 5, 32-162. | MR 1428988 | Zbl 0873.42011

[8] F. Nazarov, S. Treil, A. Volberg, Bellman function in stochastic control and harmonic analysis, in “systems, Approximation, singular Integral operators, and related topics”, ed. A. Borichev, N. Nikolski, OPERATOR THEORY : Advances and applications, v.129, 2001, 393-424, Birkhäuser Verlag. | Zbl 0999.60064

[9] F. Nazarov, A. Volberg, The Bellman function and the imbeddings of the model space K θ , to appear in J. d’Analyse Math.

[10] S. Petermichl, J. Wittwer, A sharp weighted estimates on the norm of Hilbert transform via invariant A 2 characteristic of the weight, To appear in Mich. Math. J. | MR 1897034