Tohoku Mathematical Journal
2022
June
SECOND SERIES VOL. 74, NO. 2

Tohoku Math. J.
74 (2022), 253-261

Title FRACTIONAL INTEGRATION FOR IRREGULAR MARTINGALES

Author Dmitriy Stolyarov and Dmitry Yarcev

(Received September 23, 2020, revised December 25, 2020)
Abstract. We suggest two versions of the Hardy--Littlewood--Sobolev inequality for discrete time martingales. In one version, the fractional integration operator is a martingale transform, however, it may vanish if the filtration is excessively irregular; the second version lacks the martingale property while being analytically meaningful for an arbitrary filtration.

Mathematics Subject Classification. Primary 60G42.
Key words and phrases. Fractional integration, martingales.

To the top of this page

Back to the Contents