DOI QR코드

DOI QR Code

HARDY'S INEQUALITY RELATED TO A BERNOULLI EQUATION

  • Hyun, Jung-Soon (Financial Engineering Research Center, Graduate School of Management KAIST) ;
  • Kim, Sang-Dong (Department of Mathematics Education, Kyungpook National University)
  • Published : 2002.02.01

Abstract

The weighted Hardy's inequality is known as (equation omitted) where -$\infty$$\leq$a$\leq$b$\leq$$\infty$ and 1 < p < $\infty$. The purpose of this article is to provide a useful formula to express the weight r(x) in terms of s(x) or vice versa employing a Bernoulli equation having the other weight as coefficients.

References

  1. Approximations spectrales de Problemes aux limites elliptiques C. Bernardi;Y. Maday
  2. Spectral methods in Fluid Dynamics C. Canuto;M. Y. Hussaini;A. Quarteroni;T. A. Zang
  3. Casopis Pest. Mat. v.91 Characterization of functions with zero traces by integrals with weight functions Ⅰ,Ⅱ A. Kadlec;A. Kufner
  4. Casopis Pro. v.109 Generalized Hardy's Inequality P. Gurka
  5. SIAM v.26 Numerical Analysis of Spectral Methods: Theory and Applications, CBMS-NSF Regional Conference in Applied Mathematics D. Gottlieb;S. A. Orszag
  6. Conf. Sem. Mat. Univ. Bari. v.156 Generalization of Hardy's inequality R. A. Kufner;H. Triebel
  7. Polynomial Approximation of Differential equations D. Funaro
  8. Studia Math. v.44 Hardy's Inequality with weights B. Muckenhoupt https://doi.org/10.4064/sm-44-1-31-38