MULTILINEAR INTEGRAL OPERATORS IN WEIGHTED GRAND LEBESGUE SPACES

被引：2
|
作者：
Kokilashvili, Vakhtang [1 ,2 ]
Mastylo, Mieczyslaw [3 ]
Meskhi, Alexander [1 ,4 ]
机构：
[1] I Javakhishvili Tbilisi State Univ, A Razmadze Math Inst, 6 Tamarashvili Str, GE-0177 Tbilisi, Georgia
[2] I Javakhishvili Tbilisi State Univ, Int Black Sea Univ, 3 Agmashenebeli Ave, GE-0131 Tbilisi, Georgia
[3] Adam Mickiewicz Univ, Umultowska 87, PL-61614 Poznan, Poland
[4] Georgian Tech Univ, Dept Math, Fac Informat & Control Syst, 77 Kostava St, Tbilisi, Georgia
来源：
FRACTIONAL CALCULUS AND APPLIED ANALYSIS | 2016年 / 19卷 / 03期
基金：
美国国家科学基金会;
关键词：
multisublinear maximal operators; multilinear singular integrals; one-weight inequality; grand Lebesgue space; multilinear fractional integrals; trace inequality; RIESZ FRACTIONAL INTEGRALS; INEQUALITIES; DIFFERENTIATION; BOUNDEDNESS;
D O I：
10.1515/fca-2016-0037
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The boundedness of multi(sub) linear Hardy-Littlewood maximal, Calderon-Zygmund and fractional integral operators defined on metric measure spaces is established in weighted grand Lebesgue spaces. In particular, we derive the one-weight inequality for maximal and singular integrals under the Muckenhoupt type conditions, weighted Sobolev type theorem and trace type inequality for fractional integrals.
引用
收藏
页码：696 / 724
页数：29
相关论文
共 50 条
  • [1] Multilinear integral operators in weighted grand Lebesgue spaces
    Vakhtang Kokilashvili
    Mieczysław Mastyło
    Alexander Meskhi
    [J]. Fractional Calculus and Applied Analysis, 2016, 19 : 696 - 724
  • [2] Integral operators on fully measurable weighted grand Lebesgue spaces
    Jain, Pankaj
    Singh, Monika
    Singh, Arun Pal
    [J]. INDAGATIONES MATHEMATICAE-NEW SERIES, 2017, 28 (02): : 516 - 526
  • [3] Boundedness of weighted singular integral operators in grand Lebesgue spaces
    Kokilashvili, Vakhtang
    Samko, Stefan
    [J]. GEORGIAN MATHEMATICAL JOURNAL, 2011, 18 (02) : 259 - 269
  • [4] MULTILINEAR FRACTIONAL INTEGRALS IN WEIGHTED GRAND LEBESGUE SPACES
    Kokilashvili, V.
    Mastylo, M.
    Meskhi, A.
    [J]. PROCEEDINGS OF A RAZMADZE MATHEMATICAL INSTITUTE, 2015, 169 : 143 - 153
  • [5] Boundedness of Weighted Singular Integral Operators on a Carleson Curve in Grand Lebesgue Spaces
    Kokilashvili, Vakhtang
    Samko, Stefan
    [J]. NUMERICAL ANALYSIS AND APPLIED MATHEMATICS, VOLS I-III, 2010, 1281 : 490 - +
  • [6] On integral operators in weighted grand Lebesgue spaces of Banach-valued functions
    Kokilashvili, Vakhtang
    Meskhi, Alexander
    [J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2021, 44 (12) : 9765 - 9781
  • [7] Maximal and singular integral operators in weighted grand variable exponent Lebesgue spaces
    Kokilashvili, Vakhtang
    Meskhi, Alexander
    [J]. ANNALS OF FUNCTIONAL ANALYSIS, 2021, 12 (03)
  • [8] Maximal and singular integral operators in weighted grand variable exponent Lebesgue spaces
    Vakhtang Kokilashvili
    Alexander Meskhi
    [J]. Annals of Functional Analysis, 2021, 12
  • [9] NONLINEAR HARMONIC ANALYSIS OF INTEGRAL OPERATORS IN WEIGHTED GRAND LEBESGUE SPACES AND APPLICATIONS
    Fiorenza, Alberto
    Kokilashvili, Vakhtang
    [J]. ANNALS OF FUNCTIONAL ANALYSIS, 2018, 9 (03) : 413 - 425
  • [10] Weighted Hardy Operators in Grand Lebesgue Spaces on ℝn
    Samko S.G.
    Umarkhadzhiev S.M.
    [J]. Journal of Mathematical Sciences, 2022, 268 (4) : 509 - 522
12345