RESOLVENT INEQUALITY OF LAPLACIAN IN BESOV SPACES

  • Han, Hyuk (Department of Liberal Arts, Kongju National University) ;
  • Pak, Hee Chul (Department of Applied Mathematics, Dankook University)
  • Received : 2009.03.03
  • Accepted : 2009.03.06
  • Published : 2009.03.31

Abstract

For $1{\leq}p$, $q{\leq}{\infty}$ and $s{\in}\mathbb{R}$, it is proved that there exists a constant C > 0 such that for any $f{\in}B^{s+2}_{p,q}(\mathbb{R}^n)$ $${\parallel}f{\parallel}_{B^{s+2}_{p,q}(\mathbb{R}^n)}{\leq}C{\parallel}f\;-\;{\Delta}f{\parallel}_{B^{s}_{p,q}(\mathbb{R}^n)}$$, which tells us that the operator $I-\Delta$ is $B^{s+2}_{p,q}$-coercive on the Besov space $B^s_{p,q}$.

Keywords

References

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