Geodesic
A generalization of John--Nirenberg's inequailty
Trudy Instituta matematiki, Tome 22 (2014) no. 2, pp. 63-73

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In work the generalization $BMO_\varphi$ of space of $BMO$ for functions on space of gomogeneous type that defined by integral $\varphi$-oscillations is studied. The analog of John–Nirenberg's inequality for functions from these classes is proved. As a corollary we prove coincidence of the classes $BMO_\varphi$ for rather wide class of functions $\varphi$. Furthermore, generalizations of Kampanato–Meyers's and Spanne's theorems are obtained. 
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     author = {A. I. Porabkovich and R. V. Shanin},
     title = {A generalization of {John--Nirenberg's} inequailty},
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A. I. Porabkovich; R. V. Shanin. A generalization of John--Nirenberg's inequailty. Trudy Instituta matematiki, Tome 22 (2014) no. 2, pp. 63-73. http://geodesic.mathdoc.fr/item/TIMB_2014_22_2_a6/