On a more accurate Hardy-Hilbert's inequality in the whole plane

Document Type : Research Paper


1 Department of Mathematics, Guangdong University of Education,Guangzhou, Guangdong, P.R.China

2 Department of Mathematics, Guangdong University of Education, Guangzhou, Guangdong, P.R.China


By introducing independent parameters and applying the weight coefficients, we use Hermite-Hadamard's inequality and give a more accurate Hardy-Hilbert's inequality in the whole plane with a best possible constant factor. Furthermore, the equivalent forms, a few particular cases and the operator expressions are considered.


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Volume 12, Issue 1
May 2021
Pages 1167-1179
  • Receive Date: 02 January 2018
  • Revise Date: 14 April 2018
  • Accept Date: 18 April 2018