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A sharp rearrangement inequality for the fractional maximal operator

A. Cianchi; R. Kerman; B. Opic; L. Pick — 2000

Studia Mathematica

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.

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