We prove a sharp pointwise estimate of the nonincreasing rearrangement of the fractional maximal function of ⨍, , by an expression involving the nonincreasing rearrangement of ⨍. This estimate is used to obtain necessary and sufficient conditions for the boundedness of between classical Lorentz spaces.
@article{bwmeta1.element.bwnjournal-article-smv138i3p277bwm,
author = {A. Cianchi and R. Kerman and B. Opic and L. Pick},
title = {A sharp rearrangement inequality for the fractional maximal operator},
journal = {Studia Mathematica},
volume = {141},
year = {2000},
pages = {277-284},
zbl = {0968.42014},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv138i3p277bwm}
}
Cianchi, A.; Kerman, R.; Opic, B.; Pick, L. A sharp rearrangement inequality for the fractional maximal operator. Studia Mathematica, Tome 141 (2000) pp. 277-284. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv138i3p277bwm/
[00000] [AM] M. Ariño and B. Muckenhoupt, Maximal functions on classical Lorentz spaces and Hardy's inequality with weights for nonincreasing functions, Trans. Amer. Math. Soc. 320 (1990), 727-735. | Zbl 0716.42016
[00001] [BS] C. Bennett and R. Sharpley, Interpolation of Operators, Pure Appl. Math. 129, Academic Press, New York, 1988. | Zbl 0647.46057
[00002] [OK] B. Opic and A. Kufner, Hardy-Type Inequalities, Pitman Res. Notes Math. Ser. 219, Longman Sci. & Tech., Harlow 1990. | Zbl 0698.26007
[00003] [S] E. Sawyer, Boundedness of classical operators on classical Lorentz spaces, Studia Math. 96 (1990), 145-158. | Zbl 0705.42014
[00004] [T] A. Torchinsky, Real-Variable Methods in Harmonic Analysis, Pure Appl. Math. 123, Academic Press, New York, 1986. | Zbl 0621.42001