Tohoku Mathematical Journal
2023
June
SECOND SERIES VOL. 75, NO. 2

Tohoku Math. J.
75 (2023), 161-173

Title $BLO$ CLASS UNDER THE CHANGE OF MEASURE

Author Adam Osękowski

(Received August 26, 2020, revised December 8, 2021)
Abstract. The purpose of the paper is to study the behavior of the classes of functions of bounded lower oscillation under the change of measure given by the weight $w$. More specifically, we provide sharp upper and lower bounds for the norm of the inclusion $BLO\hookrightarrow BLO(w)$ in terms of $A_\infty$ constant of the weight. The results hold in the general context of probability spaces equipped with a treelike structure.

Mathematics Subject Classification. Primary: 42B35. Secondary: 46B09.
Key words and phrases. Bounded lower oscillation, weight, Muckenhoupt class, Bellman function.

To the top of this page

Back to the Contents