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One-sided BMO spaces. (English) Zbl 0801.42010

In this paper we introduce the one-sided sharp functions defined by

f + # (x)=sup h>0 1 h x x+h f(y)-1 h x+h x+2h f + dy


f - # (x)=sup h>0 1 h x-h x f(y)-1 h x-2h x-h f + dy

where z + =max(z,0). We study the BMO spaces associated to f + # and f - # and their relation with the good weights for the one-sided Hardy-Littlewood maximal functions. Finally, as an application of our results, we characterize the weights for one-sided fractional integrals and one-sided fractional maximal operators.

42B25Maximal functions, Littlewood-Paley theory
26A33Fractional derivatives and integrals (real functions)