# A sharp rearrangement inequality for the fractional maximal operator

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

Studia Mathematica (2000)

- Volume: 138, Issue: 3, page 277-284
- ISSN: 0039-3223

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topCianchi, A., et al. "A sharp rearrangement inequality for the fractional maximal operator." Studia Mathematica 138.3 (2000): 277-284. <http://eudml.org/doc/216705>.

@article{Cianchi2000,

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.},

author = {Cianchi, A., Kerman, R., Opic, B., Pick, L.},

journal = {Studia Mathematica},

keywords = {fractional maximal operator; nonincreasing rearrangement; classical Lorentz spaces; weighted norm inequalities},

language = {eng},

number = {3},

pages = {277-284},

title = {A sharp rearrangement inequality for the fractional maximal operator},

url = {http://eudml.org/doc/216705},

volume = {138},

year = {2000},

}

TY - JOUR

AU - Cianchi, A.

AU - Kerman, R.

AU - Opic, B.

AU - Pick, L.

TI - A sharp rearrangement inequality for the fractional maximal operator

JO - Studia Mathematica

PY - 2000

VL - 138

IS - 3

SP - 277

EP - 284

AB - 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.

LA - eng

KW - fractional maximal operator; nonincreasing rearrangement; classical Lorentz spaces; weighted norm inequalities

UR - http://eudml.org/doc/216705

ER -

## References

top- [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. Zbl0716.42016
- [BS] C. Bennett and R. Sharpley, Interpolation of Operators, Pure Appl. Math. 129, Academic Press, New York, 1988. Zbl0647.46057
- [OK] B. Opic and A. Kufner, Hardy-Type Inequalities, Pitman Res. Notes Math. Ser. 219, Longman Sci. & Tech., Harlow 1990. Zbl0698.26007
- [S] E. Sawyer, Boundedness of classical operators on classical Lorentz spaces, Studia Math. 96 (1990), 145-158. Zbl0705.42014
- [T] A. Torchinsky, Real-Variable Methods in Harmonic Analysis, Pure Appl. Math. 123, Academic Press, New York, 1986. Zbl0621.42001

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