On Hardy-type integral inequalities

doi:10.1007/s10483-013-1746-x

Applied Mathematics and Mechanics (English Edition) ›› 2013, Vol. 34 ›› Issue (10): 1297-1304.doi: https://doi.org/10.1007/s10483-013-1746-x

• Articles • Previous Articles

On Hardy-type integral inequalities

LENG Tuo, FENG Yong

Chengdu Institute of Computer Applications, Chinese Academy of Sciences, Chengdu 610042, P. R. China

Received:2013-03-08 Revised:2013-03-27 Online:2013-09-29 Published:2013-09-29

Abstract

Abstract: The Hardy integral inequality is one of the most important inequalities in analysis. The present paper establishes some new Copson-Pachpatte (C-P) type inequalities, which are the generalizations of the Hardy integral inequalities on binary functions.

Key words: nanoparticles, coagulation, planar jet, moment method, large eddy simulation, Hardy inequality, Hölder inequality, Copson inequality, Izumi inequality, Pachpatte inequality

2010 MSC Number:

26D15

LENG Tuo;FENG Yong. On Hardy-type integral inequalities. Applied Mathematics and Mechanics (English Edition), 2013, 34(10): 1297-1304.

TrendMD

[1]	Y. ZHANG, M. VANIERSCHOT. Proper orthogonal decomposition analysis of coherent motions in a turbulent annular jet [J]. Applied Mathematics and Mechanics (English Edition), 2021, 42(9): 1297-1310.
[2]	Zhou YU, Hongda ZHANG, Taohong YE, Minming ZHU. Large eddy simulation of turbulent premixed piloted flame using artificial thickened flame model coupled with tabulated chemistry [J]. Applied Mathematics and Mechanics (English Edition), 2018, 39(9): 1277-1294.
[3]	Zhou YU, Hongda ZHANG, Taohong YE, Minming ZHU. Large eddy simulation of turbulent premixed and stratified combustion using flame surface density model coupled with tabulation method [J]. Applied Mathematics and Mechanics (English Edition), 2018, 39(12): 1719-1736.
[4]	Chenggong LI, J. P. Y. MAA. Multi-relaxation-time lattice Boltzmann simulations of lid driven flows using graphics processing unit [J]. Applied Mathematics and Mechanics (English Edition), 2017, 38(5): 707-722.
[5]	Mengda LIN, Guixiang CUI, Zhaoshun ZHANG. Large eddy simulation of aircraft wake vortex with self-adaptive grid method [J]. Applied Mathematics and Mechanics (English Edition), 2016, 37(10): 1289-1304.
[6]	Jianzhong LIN, Xiaojun PAN, Zhaoqin YIN, Xiaoke KU. Solution of general dynamic equation for nanoparticles in turbulent flow considering fluctuating coagulation [J]. Applied Mathematics and Mechanics (English Edition), 2016, 37(10): 1275-1288.
[7]	Man-li YANG;Zhi-ming LU;Yu-lu LIU. Self-similar behavior for multicomponent coagulation [J]. Applied Mathematics and Mechanics (English Edition), 2014, 35(11): 1353-1360.
[8]	CHEN Sheng;HUANG Xiao-Hong;YANG Chao;LIU Gang-Feng;DING Cui-Jiao;HAN Bin. Simple lattice Boltzmann approach for turbulent buoyant flow simulation [J]. Applied Mathematics and Mechanics (English Edition), 2013, 34(11): 1339-1348.
[9]	WANG Yu-Ming;LIN Jian-Zhong. Collision efficiency of two nanoparticles with different diameters in Brownian coagulation [J]. Applied Mathematics and Mechanics (English Edition), 2011, 32(8): 1019-1028.
[10]	CHEN Zhong-Li;YOU Zhen-Jiang. New expression for collision efficiency of spherical nanoparticles in Brownian coagulation [J]. Applied Mathematics and Mechanics (English Edition), 2010, 31(7): 851-860.
[11]	ZHANG Yi-Min;ZHU Li-Sha;WANG Xin-Gang. Advanced method to estimate reliability-based sensitivity of mechanical components with strongly nonlinear performance function [J]. Applied Mathematics and Mechanics (English Edition), 2010, 31(10): 1325-1336.
[12]	LIN Pei-Feng;LIN Jian-Zhong. Prediction of nanoparticle transport and deposition in bends [J]. Applied Mathematics and Mechanics (English Edition), 2009, 30(8): 957-968.
[13]	YANG Xiao-long;FU Song. Study of numerical errors in direct numerical simulation and\\ large eddy simulation [J]. Applied Mathematics and Mechanics (English Edition), 2008, 29(7): 871-880 .
[14]	YIN Zhao-qin;LIN Jian-zhong;ZHOU Kun. Research on nucleation and coagulation of nanoparticles in parallel twin jets [J]. Applied Mathematics and Mechanics (English Edition), 2008, 29(2): 153-162 .
[15]	LIU Han-dan;XU Wei;WANG Shi-gang;KE Zun-ji. Hydrodynamic modeling of ferrofluid flow in magnetic targeting drug delivery [J]. Applied Mathematics and Mechanics (English Edition), 2008, 29(10): 1341-1349 .

On Hardy-type integral inequalities

PDF

Knowledge

Cited

Abstract

Cite this article

share this article

References

Related Articles 15

Recommended Articles

Metrics

Comments