In this paper, we study the weak-type (1, 1), and strong type (p,p) ( 1 < p < + ∞) boundedness of certain Hardy-Littlewood maximal function operators. These are generated by taking the maximal averages over the left- (resp. right-) translates of various families of neighbourhoods of the identity in the affine, or "ax + b" group of the line. Investigations of this kind are basic to the study of singular integral operators. Thus, the aim of the paper is to delineate some of the positive and negative results for maximal functions on this group.
Asymmetry of maximal functions on the affine group of the line
MANTERO, ANNA MARIA;GIULINI, SAVERIO
1990-01-01
Abstract
In this paper, we study the weak-type (1, 1), and strong type (p,p) ( 1 < p < + ∞) boundedness of certain Hardy-Littlewood maximal function operators. These are generated by taking the maximal averages over the left- (resp. right-) translates of various families of neighbourhoods of the identity in the affine, or "ax + b" group of the line. Investigations of this kind are basic to the study of singular integral operators. Thus, the aim of the paper is to delineate some of the positive and negative results for maximal functions on this group.
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