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RaffaeleScandone
RaffaeleScandone
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For every $s\in(0,1)$, $\dot{H}^s(\mathbb{R}^2)$$H^s(\mathbb{R}^2)$ fails to embed into $L^p(\mathbb{R}^2)$, for some $p:=p(s)$ large enough. Hence your inequality can not be true, as BMO functions are locally $L^p$ (with a continuous embedding on bounded domains) for every $p<\infty$.

For every $s\in(0,1)$, $\dot{H}^s(\mathbb{R}^2)$ fails to embed into $L^p(\mathbb{R}^2)$, for some $p:=p(s)$ large enough. Hence your inequality can not be true, as BMO functions are locally $L^p$ (with a continuous embedding on bounded domains) for every $p<\infty$.

For every $s\in(0,1)$, $H^s(\mathbb{R}^2)$ fails to embed into $L^p(\mathbb{R}^2)$, for some $p:=p(s)$ large enough. Hence your inequality can not be true, as BMO functions are locally $L^p$ (with a continuous embedding on bounded domains) for every $p<\infty$.

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RaffaeleScandone
RaffaeleScandone
  • 282
  • 2
  • 11

For every $s\in(0,1)$, $\dot{H}^s(\mathbb{R}^2)$ fails to embed into $L^p(\mathbb{R}^2)$, for some $p:=p(s)$ large enough. Hence your inequality can not be true, as BMO functions are locally $L^p$ (with a continuous embedding on bounded domains) for every $p<\infty$.