An inquiry on Sobolev space
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Let $widetilde{H}(mathbb{R}^d) = left { f in L^2(mathbb{R}^d): G(xi)mathcal{F}f in L^2(mathbb{R}^d) right}$ and $widetilde{H}(mathbb{R}^d)$ coincides with the Sobolev space $H^beta(mathbb{R}^d)$.
Is the following relationship established?
$m {(1+{left | xi right |}_2^2)}^{beta} leq G(xi) leq M {(1+{left | xi right |}_2^2)}^{beta} quad left | xi right | > xi_0$
for some $m,M >0$ and $xi_0$.
functional-analysis sobolev-spaces
asked Dec 30 '18 at 12:10
Robin denkayRobin denkay
63
$endgroup$
add a comment |
$begingroup$
Let $widetilde{H}(mathbb{R}^d) = left { f in L^2(mathbb{R}^d): G(xi)mathcal{F}f in L^2(mathbb{R}^d) right}$ and $widetilde{H}(mathbb{R}^d)$ coincides with the Sobolev space $H^beta(mathbb{R}^d)$.
Is the following relationship established?
$m {(1+{left | xi right |}_2^2)}^{beta} leq G(xi) leq M {(1+{left | xi right |}_2^2)}^{beta} quad left | xi right | > xi_0$
for some $m,M >0$ and $xi_0$.
functional-analysis sobolev-spaces
asked Dec 30 '18 at 12:10
Robin denkayRobin denkay
63
$endgroup$
$begingroup$
What is $G$?...
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– Marvin
Dec 30 '18 at 17:43
$begingroup$
$G$ is positive real value function.
$endgroup$
– Robin denkay
Jan 2 at 13:02
add a comment |
$begingroup$
Let $widetilde{H}(mathbb{R}^d) = left { f in L^2(mathbb{R}^d): G(xi)mathcal{F}f in L^2(mathbb{R}^d) right}$ and $widetilde{H}(mathbb{R}^d)$ coincides with the Sobolev space $H^beta(mathbb{R}^d)$.
Is the following relationship established?
$m {(1+{left | xi right |}_2^2)}^{beta} leq G(xi) leq M {(1+{left | xi right |}_2^2)}^{beta} quad left | xi right | > xi_0$
for some $m,M >0$ and $xi_0$.
functional-analysis sobolev-spaces
asked Dec 30 '18 at 12:10
Robin denkayRobin denkay
63
$endgroup$
Let $widetilde{H}(mathbb{R}^d) = left { f in L^2(mathbb{R}^d): G(xi)mathcal{F}f in L^2(mathbb{R}^d) right}$ and $widetilde{H}(mathbb{R}^d)$ coincides with the Sobolev space $H^beta(mathbb{R}^d)$.
Is the following relationship established?
$m {(1+{left | xi right |}_2^2)}^{beta} leq G(xi) leq M {(1+{left | xi right |}_2^2)}^{beta} quad left | xi right | > xi_0$
for some $m,M >0$ and $xi_0$.
functional-analysis sobolev-spaces
functional-analysis sobolev-spaces
asked Dec 30 '18 at 12:10
Robin denkayRobin denkay
63
asked Dec 30 '18 at 12:10
Robin denkayRobin denkay
63
asked Dec 30 '18 at 12:10
Robin denkayRobin denkay
63
asked Dec 30 '18 at 12:10
Robin denkayRobin denkay
63
asked Dec 30 '18 at 12:10
Robin denkayRobin denkay
63
63
$begingroup$
What is $G$?...
$endgroup$
– Marvin
Dec 30 '18 at 17:43
$begingroup$
$G$ is positive real value function.
$endgroup$
– Robin denkay
Jan 2 at 13:02
add a comment |
$begingroup$
What is $G$?...
$endgroup$
– Marvin
Dec 30 '18 at 17:43
$begingroup$
$G$ is positive real value function.
$endgroup$
– Robin denkay
Jan 2 at 13:02
$begingroup$
What is $G$?...
$endgroup$
– Marvin
Dec 30 '18 at 17:43
$begingroup$
What is $G$?...
$endgroup$
– Marvin
Dec 30 '18 at 17:43
$begingroup$
$G$ is positive real value function.
$endgroup$
– Robin denkay
Jan 2 at 13:02
$begingroup$
$G$ is positive real value function.
$endgroup$
– Robin denkay
Jan 2 at 13:02
add a comment |
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$begingroup$
What is $G$?...
$endgroup$
– Marvin
Dec 30 '18 at 17:43
$begingroup$
$G$ is positive real value function.
$endgroup$
– Robin denkay
Jan 2 at 13:02