On Hardy-Littlewood-Polya and Taikov Type Inequalities for Multiple Operators in Hilbert Spaces

被引:4
|
作者
Babenko, V. [1 ]
Babenko, Yu. [2 ]
Kriachko, N. [1 ]
Skorokhodov, D. [1 ]
机构
[1] Oles Honchar Dnipro Natl Univ, Dept Math & Mech, Gagarina Pr 72, UA-49010 Dnipro, Ukraine
[2] Kennesaw State Univ, Dept Math, 1100 South Marietta Pkwy, Marietta, GA 30060 USA
基金
芬兰科学院;
关键词
Kolmogorov type inequality; Solyar type inequality; Stechkin problem; Laplace-Beltrami operator; closed operator; INTERMEDIATE DERIVATIVES; EXACT CONSTANTS;
D O I
10.1007/s10476-021-0104-8
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We present a unified approach to obtain sharp mean-squared and multiplicative inequalities of Hardy-Littlewood-Polya and Taikov types for multiple closed operators acting on Hilbert space. We apply our results to establish new sharp inequalities for the norms of powers of the Laplace-Beltrami operators on compact Riemannian manifolds and derive the well-known Taikov and Hardy-Littlewood-Polya inequalities for functions defined on the d-dimensional space in the limit case. Other applications include the best approximation of unbounded operators by linear bounded ones and the best approximation of one class by elements of another class. In addition, we establish sharp Solyar type inequalities for unbounded closed operators with closed range.
引用
收藏
页码:709 / 745
页数:37
相关论文
共 50 条
  • [1] HARDY-LITTLEWOOD-POLYA INEQUALITIES AND HAUSDORFF OPERATORS ON BLOCK SPACES
    Ho, Kwok-Pun
    MATHEMATICAL INEQUALITIES & APPLICATIONS, 2016, 19 (02): : 697 - 707
  • [2] On Hardy-Littlewood-Pólya and Taikov type inequalities for multiple operators in Hilbert spaces
    V. Babenko
    Yu. Babenko
    N. Kriachko
    D. Skorokhodov
    Analysis Mathematica, 2021, 47 : 709 - 745
  • [3] ON THE OPERATORS OF HARDY-LITTLEWOOD-POLYA TYPE
    Jin, Jianjun
    JOURNAL OF APPLIED ANALYSIS AND COMPUTATION, 2025, 15 (01): : 470 - 487
  • [4] Inequalities of Hardy-Littlewood-Polya type for functions of operators and their applications
    Babenko, Vladyslav
    Babenko, Yuliya
    Kriachko, Nadiia
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2016, 444 (01) : 512 - 526
  • [5] On exact inequalities of Hardy-Littlewood-Polya type
    Babenko, VF
    Rassias, TM
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2000, 245 (02) : 570 - 593
  • [6] Hardy-Littlewood-Polya Type Inequalities for Generalized Convex Functions
    Saleh, Khairul
    Ahmad, Izhar
    SOUTHEAST ASIAN BULLETIN OF MATHEMATICS, 2021, 45 (01) : 119 - 126
  • [7] A Multiple Hardy-Littlewood-Polya Inequality
    Sun, Baoju
    MECHATRONICS, ROBOTICS AND AUTOMATION, PTS 1-3, 2013, 373-375 : 1906 - 1909
  • [8] REVERSED HARDY-LITTLEWOOD-POLYA INEQUALITIES WITH FINITE TERMS
    Han, Haiyan
    Lei, Yutian
    BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2023, 108 (03) : 459 - 463
  • [9] Generalizations of Some Hardy-Littlewood-Polya Type Inequalities and Related Results
    Khalid, Sadia
    Pecaric, Josip
    FILOMAT, 2021, 35 (08) : 2811 - 2826
  • [10] A MULTIPLE MORE ACCURATE HARDY-LITTLEWOOD-POLYA INEQUALITY
    Huang, Qiliang
    Yang, Bicheng
    Debnath, Lokenath
    MATEMATICHE, 2012, 67 (02): : 93 - 105