Estimates of Oscillations of the Hardy Transform

A. A. Korenovskii

National Taras Shevchenko University of Kyiv

Abstract: 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.

UDC: 517.5

Received: 29.03.2001
Revised: 10.01.2002

DOI: 10.4213/mzm430

 English version: Mathematical Notes, 2002, 72:3, 350–361

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