A sharp rearrangement inequality for the fractional maximal operator
Volume 138 / 2000
Studia Mathematica 138 (2000), 277-284
DOI: 10.4064/sm-138-3-277-284
Abstract
We prove a sharp pointwise estimate of the nonincreasing rearrangement of the fractional maximal function of ⨍, $M_{γ}⨍$, by an expression involving the nonincreasing rearrangement of ⨍. This estimate is used to obtain necessary and sufficient conditions for the boundedness of $M_γ$ between classical Lorentz spaces.
