Geodesic
The Bellman functions for a certain two-weight inequality: A case study
Algebra i analiz, Tome 18 (2006) no. 2, pp. 24-56 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A formula is presented for the exact Bellman function of a certain “toy” two-weight problem. This adds one more function to a short list of other Bellman functions for which the precise expressions have recently been found. The case study reveals essential features of finding Bellman functions in general and gives the extremal sequences for the problem. Some open questions are posed. 
@article{AA_2006_18_2_a1,
     author = {V. Vasyunin and A. Vol'berg},
     title = {The {Bellman} functions for a certain two-weight inequality: {A~case} study},
     journal = {Algebra i analiz},
     pages = {24--56},
     year = {2006},
     volume = {18},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AA_2006_18_2_a1/}
}
TY  - JOUR
AU  - V. Vasyunin
AU  - A. Vol'berg
TI  - The Bellman functions for a certain two-weight inequality: A case study
JO  - Algebra i analiz
PY  - 2006
SP  - 24
EP  - 56
VL  - 18
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/AA_2006_18_2_a1/
LA  - ru
ID  - AA_2006_18_2_a1
ER  - 
%0 Journal Article
%A V. Vasyunin
%A A. Vol'berg
%T The Bellman functions for a certain two-weight inequality: A case study
%J Algebra i analiz
%D 2006
%P 24-56
%V 18
%N 2
%U http://geodesic.mathdoc.fr/item/AA_2006_18_2_a1/
%G ru
%F AA_2006_18_2_a1
V. Vasyunin; A. Vol'berg. The Bellman functions for a certain two-weight inequality: A case study. Algebra i analiz, Tome 18 (2006) no. 2, pp. 24-56. http://geodesic.mathdoc.fr/item/AA_2006_18_2_a1/

[B] Burkholder D. L., “Explorations in martingale theory and its applications”, École d'Été de Probabilités de Saint-Flour XIX–1989, Lecture Notes in Math., 1464, Springer, Berlin, 1991, 1–66 | MR

[CS] Cotlar M., Sadosky C., “On the Helson–Szegö theorem and a related class of modified Toeplitz kernels”, Harmonic Analysis in Euclidean spaces, part 1 (Proc. Sympos. Pure Math., Williams Coll., Williamstown, MA, 1978), Proc. Sympos. Pure Math., 35, eds. G. Weiss and S. Wainger, Amer. Math. Soc., Providence, RI, 1979, 383–407 | MR

[N] Nazarov F., A counterexample to a problem of Sarason on boundedness of the product of two Toeplitz operators, Preprint, 1996, pp. 1–5

[NTV1] Nazarov F., Treil S., Volberg A., “The Bellman functions and two-weight inequalities for Haar multipliers”, J. Amer. Math. Soc., 12 (1999), 909–928 | DOI | MR | Zbl

[NTV2] Nazarov F., Treil S., Volberg A., The T1 theorem for individual Haar multiplier, preprint, 2004

[NV] Nazarov F., Volberg A., “The Bellman function, two weighted Hilbert transform, and embeddings of the model spaces $K_\theta$”, Dedicated to the memory of Thomas H. Wolff, J. Anal. Math., 87 (2002), 385–414 | DOI | MR | Zbl

[S1] Sawyer E. T., “A characterization of a two-weight norm inequality for maximal operators”, Studia Math., 75 (1982), 1–11 | MR | Zbl

[S2] Sawyer E. T., “A characterization of two weight norm inequality for fractional and Poisson integrals”, Trans. Amer. Math. Soc., 308 (1988), 533–545 | DOI | MR | Zbl