Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I'm not able to prove the following inequality: Fix $s>0$

$$\|fg\|_{H^s}\lesssim \|fJ^sg\|_{L^2}+\|gJ^sf\|_{L^2},$$ where $\widehat{J^sf}(\xi)=(1+|\xi|^2)^{s/2}\hat{f}(\xi)$ (Bessel potential).

Actually, I used the inequality $(1+|\xi|^2)^{s/2}\lesssim (1+|\xi-y|^2)^{s/2}+(1+|y|^2)^{s/2}$ (obvious), to "spread" the weight in the convolution, but I had problems to finish.

share|cite|improve this question

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.