Geodesic
On the Bellman function method for operators on martingales
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 498 (2021), pp. 27-30

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It is shown how to apply the Bellman function method to general operators on martingales, i.e., to operators that are not necessarily martingale transforms. As examples of such operators, we consider the Haar transforms and an operator whose $L^p$-boundedness implies the Rubio de Francia inequality for the Walsh system. For the corresponding Bellman function, the Bellman induction is carried out and a Bellman candidate is constructed.
Keywords: Burkholder method, Gundy theorem, Walsh system, Rubio de Francia inequality, Haar transform. 
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     author = {V. A. Borovitskii and N. N. Osipov and A. S. Tselishchev},
     title = {On the {Bellman} function method for operators on martingales},
     journal = {Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleni\^a},
     pages = {27--30},
     publisher = {mathdoc},
     volume = {498},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DANMA_2021_498_a4/}
}
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V. A. Borovitskii; N. N. Osipov; A. S. Tselishchev. On the Bellman function method for operators on martingales. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 498 (2021), pp. 27-30. http://geodesic.mathdoc.fr/item/DANMA_2021_498_a4/