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http://dx.doi.org/10.14403/jcms.2013.26.1.105

LOGARITHMIC COMPOSITION INEQUALITY IN BESOV SPACES  

Park, Young Ja (Department of Mathematics Hoseo University)
Publication Information
Journal of the Chungcheong Mathematical Society / v.26, no.1, 2013 , pp. 105-110 More about this Journal
Abstract
A logarithmic composition inequality in Besov spaces is derived which generalizes Vishik's inequality: ${\parallel}f{\circ}g{\parallel}_{B^s_{p,1}}{\leq}(1+{\log}({\parallel}{\nabla}g{\parallel}_{L^{\infty}}{\parallel}{\nabla}g^{-1}{\parallel}_{L^{\infty}})){\parallel}f{\parallel}_{B^s_{p,1}}$, where $g$ is a volume-preserving diffeomorphism on ${\mathbb{R}}^n$.
Keywords
logarithmic inequality; Euler equations; Besov spaces;
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