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

Abstract

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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.

How to cite

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Cianchi, 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

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  1. [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
  2. [BS] C. Bennett and R. Sharpley, Interpolation of Operators, Pure Appl. Math. 129, Academic Press, New York, 1988. Zbl0647.46057
  3. [OK] B. Opic and A. Kufner, Hardy-Type Inequalities, Pitman Res. Notes Math. Ser. 219, Longman Sci. & Tech., Harlow 1990. Zbl0698.26007
  4. [S] E. Sawyer, Boundedness of classical operators on classical Lorentz spaces, Studia Math. 96 (1990), 145-158. Zbl0705.42014
  5. [T] A. Torchinsky, Real-Variable Methods in Harmonic Analysis, Pure Appl. Math. 123, Academic Press, New York, 1986. Zbl0621.42001

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