1.
Buckley, S. M., Estimates for operator norms on weighted spaces and reverse Jensen inequalities. Trans. Amer. Math. Soc.
340(1) 1993, 253–272.

2.
Burkholder, D. L., Boundary value problems and sharp inequalities for martingale transforms. Ann. Probab.
12
1984, 647–702.

3.
Dellacherie, C. and Meyer, P.-A., Probabilities and Potential B: Theory of Martingales, North-Holland (Amsterdam, 1982).

4.
Fefferman, C. and Stein, E. M., Some maximal inequalities. Amer. J. Math.
93
1971, 107–115.

5.
Izumisawa, M. and Kazamaki, N., Weighted norm inequalities for martingales. Tohoku Math. J. (2)
29
1977, 115–124.

6.
Kazamaki, N., Continuous Exponential Martingales and BMO
(*Lecture Notes in Mathematics ***1579**
), Springer (Berlin, 1994).

7.
Lerner, A. K., Ombrosi, S. and Pérez, C., Sharp *A*
_{1} bounds for Calderón–Zygmund operators and the relationship with a problem of Muckenhoupt and Wheeden. Int. Math. Res. Not. IMRN
6
2008, Art. ID rnm161, 11 p.

8.
Lerner, A. K., Ombrosi, S. and Pérez, C.,
*A*
_{1} bounds for Calderón–Zygmund operators related to a problem of Muckenhoupt and Wheeden. Math. Res. Lett.
16
2009, 149–156.

9.
Nazarov, F. L., Reznikov, A., Vasyunin, V. and Volberg, A., A Bellman function counterexample to the
$A_{1}$
conjecture: the blow-up of the weak norm estimates of weighted singular operators. *Preprint*, 2015, arXiv:1506.04710.
10.
Nazarov, F. L. and Treil, S. R., The hunt for a Bellman function: applications to estimates for singular integral operators and to other classical problems of harmonic analysis. St. Petersburg Math. J.
8
1997, 721–824.

11.
Nazarov, F. L., Treil, S. R. and Volberg, A., The Bellman functions and two-weight inequalities for Haar multipliers. J. Amer. Math. Soc.
12
1999, 909–928.

12.
Obłój, J., The Skorokhod embedding problem and its offspring. Probab. Surv.
1
2004, 321–392.

13.
Osȩkowski, A., Sharp Martingale and Semimartingale Inequalities
(*Monografie Matematyczne ***72**
), Birkhäuser (Basel, 2012), 462 pp.

14.
Petermichl, S. and Wittwer, J., A sharp estimate for the weighted Hilbert transform via Bellman functions. Michigan Math. J.
50
2002, 71–87.

15.
Reguera, M. C., On Muckenhoupt–Wheeden conjecture. Adv. Math.
227(4) 2011, 1436–1450.

16.
Reguera, M. C. and Thiele, C., The Hilbert transform does not map *L*
^{1}(*Mw*) to *L*
^{1, ∞
}(*w*). Math. Res. Lett.
19(1) 2012, 1–7.

17.
Slavin, L. and Vasyunin, V., Sharp results in the integral-form John–Nirenberg inequality. Trans. Amer. Math. Soc.
363
2011, 4135–4169.

18.
Vasyunin, V. and Volberg, A., Monge–Ampére equation and Bellman optimization of Carleson Embedding Theorems. In Linear and Complex Analysis
(*American Mathematical Society Translations (2) ***226**
), American Mathematical Society (Providence, RI, 2009), 195–238.