Inequality of logarithm function in terms of $L^p$ norm
Clash Royale CLAN TAG#URR8PPP
up vote
1
down vote
favorite
I am struggling to show that
for $fin L^q([0,1])$ with $q>0$,
$int_[0,1]log|f|dmleq logleft| f right|_q $.
I even don't know how to start :( Hope I can get some help :)
real-analysis analysis lp-spaces
add a comment |Â
up vote
1
down vote
favorite
I am struggling to show that
for $fin L^q([0,1])$ with $q>0$,
$int_[0,1]log|f|dmleq logleft| f right|_q $.
I even don't know how to start :( Hope I can get some help :)
real-analysis analysis lp-spaces
1
Just apply Jensen.
â Shalop
Aug 7 at 19:39
@Shalop That works! Thank you!
â Lev Ban
Aug 7 at 19:40
add a comment |Â
up vote
1
down vote
favorite
up vote
1
down vote
favorite
I am struggling to show that
for $fin L^q([0,1])$ with $q>0$,
$int_[0,1]log|f|dmleq logleft| f right|_q $.
I even don't know how to start :( Hope I can get some help :)
real-analysis analysis lp-spaces
I am struggling to show that
for $fin L^q([0,1])$ with $q>0$,
$int_[0,1]log|f|dmleq logleft| f right|_q $.
I even don't know how to start :( Hope I can get some help :)
real-analysis analysis lp-spaces
edited Aug 7 at 19:27
asked Aug 7 at 17:59
Lev Ban
48616
48616
1
Just apply Jensen.
â Shalop
Aug 7 at 19:39
@Shalop That works! Thank you!
â Lev Ban
Aug 7 at 19:40
add a comment |Â
1
Just apply Jensen.
â Shalop
Aug 7 at 19:39
@Shalop That works! Thank you!
â Lev Ban
Aug 7 at 19:40
1
1
Just apply Jensen.
â Shalop
Aug 7 at 19:39
Just apply Jensen.
â Shalop
Aug 7 at 19:39
@Shalop That works! Thank you!
â Lev Ban
Aug 7 at 19:40
@Shalop That works! Thank you!
â Lev Ban
Aug 7 at 19:40
add a comment |Â
1 Answer
1
active
oldest
votes
up vote
1
down vote
Hint:
- $forall p>0, forall qin(p,+infty), |f|_ple|f|_q$;
- $lim_qrightarrow 0^+ |f|_q=expleft(int_[0,1]log|f(t)|operatornamedtright)$
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
Hint:
- $forall p>0, forall qin(p,+infty), |f|_ple|f|_q$;
- $lim_qrightarrow 0^+ |f|_q=expleft(int_[0,1]log|f(t)|operatornamedtright)$
add a comment |Â
up vote
1
down vote
Hint:
- $forall p>0, forall qin(p,+infty), |f|_ple|f|_q$;
- $lim_qrightarrow 0^+ |f|_q=expleft(int_[0,1]log|f(t)|operatornamedtright)$
add a comment |Â
up vote
1
down vote
up vote
1
down vote
Hint:
- $forall p>0, forall qin(p,+infty), |f|_ple|f|_q$;
- $lim_qrightarrow 0^+ |f|_q=expleft(int_[0,1]log|f(t)|operatornamedtright)$
Hint:
- $forall p>0, forall qin(p,+infty), |f|_ple|f|_q$;
- $lim_qrightarrow 0^+ |f|_q=expleft(int_[0,1]log|f(t)|operatornamedtright)$
answered Aug 7 at 19:36
Bob
1,489522
1,489522
add a comment |Â
add a comment |Â
Â
draft saved
draft discarded
Â
draft saved
draft discarded
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2875212%2finequality-of-logarithm-function-in-terms-of-lp-norm%23new-answer', 'question_page');
);
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
1
Just apply Jensen.
â Shalop
Aug 7 at 19:39
@Shalop That works! Thank you!
â Lev Ban
Aug 7 at 19:40