충청수학회지 (Journal of the Chungcheong Mathematical Society)

  • 제22권1호
  • /
  • Pages.117-121
  • /
  • 2009
  • /
  • 1226-3524(pISSN)
  • /
  • 2383-6245(eISSN)
충청수학회 (The Chungcheong Mathematical Society)
권호 표지

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)
  • 투고 : 2009.03.03
  • 심사 : 2009.03.06
  • 발행 : 2009.03.31
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초록

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 $B^s_{p,q}$.

키워드

참고문헌

  1. J. Y. Chemin, Perfect incompressible fluids, Clarendon Press, Oxford, 1981.
  2. H-C Pak and Y. J. Park, Existence of solution for the Euler equations in a critical Besov space $B^{1}_{\infty},1(R^{n})$, Comm. P.D.E. 29 (2004), 1149-1166. https://doi.org/10.1081/PDE-200033764
  3. E.M. Stein, Harmonic analysis; Real-variable methods, orthogonality, and osillatory integrals, Princeton Mathematical Series, Vol. 43, 1993.
  4. H. Triebel, Theory of Function spaces II, Birkhauser, 1992.
  5. M.E. Taylor, Tools for PDE Pseudodifferential Operators, Para-differential Operators, and Layer Potentials, Mathematical surveys and Monographs, Vol. 81, American Mathematical Society, 2000.