A class of Hilbert-type multiple integral inequalities with the kernel of generalized homogeneous function and its applications-Reference-Cited by-同舟云学术

A class of Hilbert-type multiple integral inequalities with the kernel of generalized homogeneous function and its applications

Published:2020-05-13 Issue:1 Volume:2020 Page:
ISSN:1029-242X
Container-title:Journal of Inequalities and Applications
language:en
Short-container-title:J Inequal Appl

Author:

Hong Yong,Liao Jianquan^ORCID,Yang Bicheng,Chen Qiang

Abstract

AbstractLet

$x=(x_{1},x_{2},\ldots,x_{n})$

x=(x1,x2,…,xn), and let

$K(u(x),v(y))$

K(u(x),v(y)) satisfy

$u(rx)=ru(x)$

u(rx)=ru(x),

$v(ry)=rv(y)$

v(ry)=rv(y),

$K(ru,v)=r^{\lambda\lambda_{1}}K(u, r^{-\frac{\lambda_{1}}{\lambda_{2}}}v)$

K(ru,v)=rλλ1K(u,r−λ1λ2v), and

$K(u,rv)=r^{\lambda\lambda_{2}}K(r^{-\frac{\lambda_{2}}{\lambda_{1}}}u, v)$

K(u,rv)=rλλ2K(r−λ2λ1u,v). In this paper, we obtain a necessary and sufficient condition and the best constant factor for the Hilbert-type multiple integral inequality with kernel

$K(u(x),v(y))$

K(u(x),v(y)) and discuss its applications in the theory of operators.

Funder

National Natural Science Foundation of China

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis

Link

https://link.springer.com/content/pdf/10.1186/s13660-020-02401-0.pdf

Reference17 articles.

1. Hong, Y.: A Hilbert-type integral inequality with quasi-homogeneous kernel and several functions. Acta Math. Sin. Chin. Ser., 57, 833–840 (2014)

2. He, B., Cao, J.F., Yang, B.C.: A brand new multiple Hilbert-type integral inequality. Acta Math. Sin. Chin. Ser. 58, 661–672 (2015)

3. Perić, I., Vuković, P.: Hardy–Hilbert’s inequalities with a general homogeneous kernel. Math. Inequal. Appl. 12, 525–536 (2009)

4. Yang, B.C.: On an extension of Hilbert’s integral inequality with some parameters. Aust. J. Math. Anal. Appl. 1(1), 1–8 (2004)

5. Hong, Y., Wen, Y.M.: A necessary and sufficient condition of that Hilbert type series inequality with homogeneous kernel and the best constant factor. Chin. Ann. Math. 37A(3), 329–336 (2017)

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