Skip to main content

Extensions of Hardy inequality

Abstract

We study extended Hardy inequalities using Littlewood-Paley theory and nonlinear estimates' method in Besov spaces. Our results improve and extend the well-known results of Cazenave (2003).

[123456]

References

  1. 1.

    Bergh J, Löfström J: Interpolation Spaces. An Introduction. Springer, Berlin; 1976:x+207.

    Google Scholar 

  2. 2.

    Cazenave T: Semilinear Schrödinger Equations, Courant Lecture Notes in Mathematics. Volume 10. American Mathematical Society, Rhode Island; 2003:xiv+323.

    Google Scholar 

  3. 3.

    Lemarié-Rieusset PG: Recent Developments in the Navier-Stokes Problem, Chapman & Hall/CRC Research Notes in Mathematics. Volume 431. Chapman & Hall/CRC, Florida; 2002:xiv+395.

    Google Scholar 

  4. 4.

    Miao C: Harmonic Analysis and Application to Differential Equations. 2nd edition. Science Press, Beijing; 2004.

    Google Scholar 

  5. 5.

    Runst T, Sickel W: Sobolev Spaces of Fractional Order, Nemytskij Operators, and Nonlinear Partial Differential Equations, de Gruyter Series in Nonlinear Analysis and Applications. Volume 3. Walter de Gruyter, Berlin; 1996:x+547.

    Google Scholar 

  6. 6.

    Triebel H: Interpolation Theory, Function Spaces, Differential Operators, North-Holland Mathematical Library. Volume 18. North-Holland, Amsterdam; 1978:528.

    Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Junyong Zhang.

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Reprints and Permissions

About this article

Cite this article

Zhang, J. Extensions of Hardy inequality. J Inequal Appl 2006, 69379 (2006). https://doi.org/10.1155/JIA/2006/69379

Download citation

Keywords

  • Besov Space
  • Nonlinear Estimate
  • Hardy Inequality
\