A sharp rearrangement inequality for the fractional maximal operator

被引：0

作者：

Cianchi, A

Kerman, R

Opic, B

Pick, L

机构：

[1] Univ Florence, Fac Architettura, Ist Matemat, I-50122 Florence, Italy

[2] Acad Sci Czech Republ, Inst Math, CR-11567 Prague 1, Czech Republic

[3] Brock Univ, Dept Math, St Catharines, ON L2S 3A1, Canada

[4] Charles Univ, Fac Math & Phys, Dept Math Anal, Prague 18675 8, Czech Republic

来源：

STUDIA MATHEMATICA | 2000年 / 138卷 / 03期

关键词：

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

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove a sharp pointwise estimate of the nonincreasing rearrangement of the fractional maximal function of f, M-gamma f, by an expression involving the nonincreasing rearrangement of f. This estimate is used to obtain necessary and sufficient conditions for the boundedness of M-gamma between classical Lorentz spaces.

引用

页码：277 / 284

页数：8

共 50 条

[1] A sharp integral rearrangement inequality for the dyadic maximal operator and applications
Nikolidakis, Eleftherios N.
Melas, Antonios D.
APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS, 2015, 38 (02) : 242 - 261
[2] Rearrangement inequality for the Hardy–Littlewood maximal operator
Xudong Nie
Dunyan Yan
Shao Liu
Yangkendi Deng
Banach Journal of Mathematical Analysis, 2022, 16
[3] Rearrangement inequality for the Hardy-Littlewood maximal operator
Nie, Xudong
Yan, Dunyan
Liu, Shao
Deng, Yangkendi
BANACH JOURNAL OF MATHEMATICAL ANALYSIS, 2022, 16 (03)
[4] A SHARP INTEGRAL INEQUALITY FOR THE DYADIC MAXIMAL OPERATOR AND A RELATED STABILITY RESULT
Nikolidakis, Eleftherios N.
ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA, 2020, 45 : 533 - 546
[5] OPTIMAL COUPLES OF REARRANGEMENT INVARIANT SPACES FOR THE FRACTIONAL MAXIMAL OPERATOR
Ahmed, Irshaad
Karadzhov, Georgi
Nazeer, Waqas
COMPTES RENDUS DE L ACADEMIE BULGARE DES SCIENCES, 2011, 64 (09): : 1233 - 1240
[6] Sharp maximal inequality for stochastic integrals
Osekowski, Adam
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2008, 136 (08) : 2951 - 2958
[7] Sharp maximal inequality for nonnegative martingales
Osekowski, Adam
STATISTICS & PROBABILITY LETTERS, 2011, 81 (12) : 1945 - 1952
[8] A SHARP ESTIMATE IN AN OPERATOR-INEQUALITY
MCEACHIN, R
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1992, 115 (01) : 161 - 165
[9] A WEIGHTED INEQUALITY FOR THE KAKEYA MAXIMAL OPERATOR
VARGAS, AM
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1994, 120 (04) : 1101 - 1105
[10] SHARP MAXIMAL INEQUALITY FOR MARTINGALES AND STOCHASTIC INTEGRALS
Osekowski, Adam
ELECTRONIC COMMUNICATIONS IN PROBABILITY, 2009, 14 : 17 - 30

← 1 2 3 4 5 →