Mixing
A type of reverse Holder inequality
Let $D={phi_i}_{i=1}^N$ be an orthonormal set in $L_2[0,1]$, $u(x)in operatorname{Span}{D}$. Let $mu(x)$ be a density function on $[0,1]$. Under what condition can we say $int_{0}^1 u(x)^4 dmu(x)leq cleft(int_0^1 u(x)^2 dmu(x)right)^2$ for some constant $c$?
An answer with imposing additional condition on $mu(x)$ is:
$L^{p}$ inequality with a lower bound on measure
I am wondering if we impose some conditions on ${phi_i}_{i=1}^N$, can we still get the same type of argument?
Thanks!
functional-analysis measure-theory lp-spaces
edited Dec 31 '18 at 21:18
Davide Giraudo
125k16150261
asked Dec 30 '18 at 20:44
user348207user348207
182
add a comment |
Let $D={phi_i}_{i=1}^N$ be an orthonormal set in $L_2[0,1]$, $u(x)in operatorname{Span}{D}$. Let $mu(x)$ be a density function on $[0,1]$. Under what condition can we say $int_{0}^1 u(x)^4 dmu(x)leq cleft(int_0^1 u(x)^2 dmu(x)right)^2$ for some constant $c$?
An answer with imposing additional condition on $mu(x)$ is:
$L^{p}$ inequality with a lower bound on measure
I am wondering if we impose some conditions on ${phi_i}_{i=1}^N$, can we still get the same type of argument?
Thanks!
functional-analysis measure-theory lp-spaces
edited Dec 31 '18 at 21:18
Davide Giraudo
125k16150261
asked Dec 30 '18 at 20:44
user348207user348207
182
add a comment |
Let $D={phi_i}_{i=1}^N$ be an orthonormal set in $L_2[0,1]$, $u(x)in operatorname{Span}{D}$. Let $mu(x)$ be a density function on $[0,1]$. Under what condition can we say $int_{0}^1 u(x)^4 dmu(x)leq cleft(int_0^1 u(x)^2 dmu(x)right)^2$ for some constant $c$?
An answer with imposing additional condition on $mu(x)$ is:
$L^{p}$ inequality with a lower bound on measure
I am wondering if we impose some conditions on ${phi_i}_{i=1}^N$, can we still get the same type of argument?
Thanks!
functional-analysis measure-theory lp-spaces
edited Dec 31 '18 at 21:18
Davide Giraudo
125k16150261
asked Dec 30 '18 at 20:44
user348207user348207
182
Let $D={phi_i}_{i=1}^N$ be an orthonormal set in $L_2[0,1]$, $u(x)in operatorname{Span}{D}$. Let $mu(x)$ be a density function on $[0,1]$. Under what condition can we say $int_{0}^1 u(x)^4 dmu(x)leq cleft(int_0^1 u(x)^2 dmu(x)right)^2$ for some constant $c$?
An answer with imposing additional condition on $mu(x)$ is:
$L^{p}$ inequality with a lower bound on measure
I am wondering if we impose some conditions on ${phi_i}_{i=1}^N$, can we still get the same type of argument?
Thanks!
functional-analysis measure-theory lp-spaces
functional-analysis measure-theory lp-spaces
edited Dec 31 '18 at 21:18
Davide Giraudo
125k16150261
asked Dec 30 '18 at 20:44
user348207user348207
182
edited Dec 31 '18 at 21:18
Davide Giraudo
125k16150261
asked Dec 30 '18 at 20:44
user348207user348207
182
edited Dec 31 '18 at 21:18
Davide Giraudo
125k16150261
edited Dec 31 '18 at 21:18
Davide Giraudo
125k16150261
edited Dec 31 '18 at 21:18
Davide Giraudo
125k16150261
125k16150261
asked Dec 30 '18 at 20:44
user348207user348207
182
asked Dec 30 '18 at 20:44
user348207user348207
182
asked Dec 30 '18 at 20:44
user348207user348207
182
182
add a comment |
add a comment |
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