Geodesic
Estimates of Oscillations of the Hardy Transform
Matematičeskie zametki, Tome 72 (2002) no. 3, pp. 383-395

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For the Hardy transform of a nonincreasing function we obtain a sharp two-sided estimate of the $\operatorname {BLO}$-norm and sharp inequalities between the $\operatorname {BMO}$- and the $\operatorname {BLO}$-norms of a nonincreasing function. A well-known lower bound for the $\operatorname {BMO}$-norm of the Hardy transform is improved on the basis of these inequalities. 
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     author = {A. A. Korenovskii},
     title = {Estimates of {Oscillations} of the {Hardy} {Transform}},
     journal = {Matemati\v{c}eskie zametki},
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     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2002_72_3_a6/}
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A. A. Korenovskii. Estimates of Oscillations of the Hardy Transform. Matematičeskie zametki, Tome 72 (2002) no. 3, pp. 383-395. http://geodesic.mathdoc.fr/item/MZM_2002_72_3_a6/