Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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POINCARÉ'S INEQUALITY ON A NEW FUNCTION SPACE Lα(X)

  • Pak, Hee Chul (Department of Applied Mathematics and Institute of Basic Sciences Dankook University) ;
  • Chang, Sang-Hoon (Department of Applied Mathematics Dankook University)
  • Received : 2009.04.19
  • Accepted : 2009.05.26
  • Published : 2009.09.30
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Abstract

We prove the homogeneous property of the norm of the new space $L\alpha(X)$ which has been developed in [3]. We also present $Poincar\acute{e}^{\prime}s$ inequality that is fitted to the function space $L\alpha(X)$ with an appropriate slope condition.

Keywords

References

  1. G. Folland, Real Analysis, John Wiley & Sons, Inc., 1984.
  2. E. H. Lieb and M. Loss, Analysis, 2nd edition, volume 14 of Graduate studies in mathematics, AMS, 2001.
  3. H.-C. Pak and S.-H. Chang, A New function space $L_{\alpha}$(X)- Version 1.1, J. Chung-cheong Math. soc. 21 (2008), 471-481.
  4. H.-C. Pak, Y.-J. Park and S.-H. Chang, Existence of solutions for a nonlinear Dirichlet problem in a new function space, To appear.
  5. R. E. Showalter, Monotone Operators in Banach Space and Nonlinear Partial Differential Equations, volume 49 of Mathematical Surveys and Monographs, AMS, 1997.