Norm inequalities for some one-sided operators

Abstract

We show that the one-sided maximal operators associated with Borel measures are of strong type (p, p) , 1 < p < ∞ , with constant p∗ , and the related one-sided geometric maximal operators are of strong type (p, p) , 0 < p < ∞ , with constant e1/p . We also investigate norm inequalities for integral operators with three measures on the cone of nonnegative nonincreasing functions. Our results show that if we restrict the measures in the inequalities to some particular classes, then a simple characterization for these inequalities to hold can be obtained. Mathematics subject classification (2010): Primary 26D15; Secondary 26D10, 42B25.