0
$\begingroup$

This question already has an answer here:

How to prove that $L^p$ space is a subset of $L^q$ space whenever $1 \leq p \leq q < \infty$?

I tried to solve it using the $L^p$ space definition. Tell me how to proceed further?

$\endgroup$

marked as duplicate by tomasz, user91500, user370967, Davide Giraudo, kingW3 Jun 23 '17 at 11:20

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

  • $\begingroup$ your statement is however true for "little" lp and "little" lq spaces (the spaces of convergent series). $\endgroup$ – user135891 Mar 30 '14 at 16:21
3
$\begingroup$

This isn't true. Consider $f(x) = \frac 1{\sqrt x}$ which is in $L^1[0,1]$ but not in $L^2[0,1]$ .

$\endgroup$

Not the answer you're looking for? Browse other questions tagged or ask your own question.