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
收藏
页码：277 / 284
页数：8
相关论文
共 50 条
  • [41] A WEIGHTED INEQUALITY FOR A DYADIC-LIKE MAXIMAL OPERATOR
    Rapicki, M.
    ANALYSIS MATHEMATICA, 2018, 44 (04) : 577 - 585
  • [42] A modular variable Orlicz inequality for the local maximal operator
    Capone, Claudia
    Cruz-Uribe, David
    Fiorenza, Alberto
    GEORGIAN MATHEMATICAL JOURNAL, 2018, 25 (02) : 201 - 206
  • [43] Weighted norm inequality for a maximal operator on homogeneous space
    Fernandes, Iara A. A.
    Tozoni, Sergio A.
    ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN, 2008, 27 (01): : 67 - 78
  • [44] GRONWALL INEQUALITY FOR A GENERAL CAPUTO FRACTIONAL OPERATOR
    Almeida, Ricardo
    MATHEMATICAL INEQUALITIES & APPLICATIONS, 2017, 20 (04): : 1089 - 1105
  • [45] On a Hardy's inequality for a fractional integral operator
    Hernandez Hernandez, Jorge Eliecer
    Vivas Cortez, Miguel Jose
    ANNALS OF THE UNIVERSITY OF CRAIOVA-MATHEMATICS AND COMPUTER SCIENCE SERIES, 2018, 45 (02): : 232 - 242
  • [46] Some local Poincare inequalities for the composition of the sharp maximal operator and the Green's operator
    Yi Ling
    Bao Gejun
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2012, 63 (03) : 720 - 727
  • [47] REARRANGEMENT, MAXIMAL INEQUALITIES AND FRACTIONAL ERGODIC-THEOREMS
    BROISE, M
    DENIEL, Y
    DERRIENNIC, Y
    ANNALES DE L INSTITUT FOURIER, 1989, 39 (03) : 689 - 714
  • [48] COMMUTATORS FOR THE FRACTIONAL MAXIMAL AND SHARP FUNCTIONS ON TOTAL MORREY SPACES
    Xue, Fengyu
    PROCEEDINGS OF THE ROMANIAN ACADEMY SERIES A-MATHEMATICS PHYSICS TECHNICAL SCIENCES INFORMATION SCIENCE, 2024, 25 (02): : 103 - 110
  • [49] MIXED WEAK TYPE INEQUALITIES FOR THE FRACTIONAL MAXIMAL OPERATOR
    Lorente, Maria
    Martin-Reyes, Francisco J.
    REVISTA DE LA UNION MATEMATICA ARGENTINA, 2023, 66 (01): : 229 - 242
  • [50] BOUNDEDNESS FOR A CLASS OF FRACTIONAL CARLESON TYPE MAXIMAL OPERATOR
    Yu, Xiao
    Zhang, Huihui
    Wu, Xiaomei
    JOURNAL OF MATHEMATICAL INEQUALITIES, 2020, 14 (03): : 707 - 721
12345