1
$\begingroup$

Specificaly:

  • Does convergence in $L^{\frac{1}{2}}$ imply weak $L^2$ convergence?

  • Having a limit in $L^{\frac{1}{2}}$ topology and a limit in weak $L^2$ topology whether these are always equal? If not, what additional assumption would enable the conclusion?

Generally:

  • Whether strong $L^q$ topology is finer (stronger) than a weak $L^p$ topology for some $q<p$?
$\endgroup$

Your Answer

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Browse other questions tagged or ask your own question.