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

A typical way to show $L^{p}$ boundedness of a linear or sub-linear operator is to show a weak type $(1,1)$ bound and an $L^{p}$ bound for some $p$, and then combine these two using interpolation to prove $L^{p}$ bounds for all $p$ between $1$ and $\infty$. A typical example is that of the Hardy-Littlewood maximal Operator. Are there any examples\techniques where $L^{p}$ boundedness is proved without establishing some type of weak type bounds?

share|cite|improve this question

One can work directly with $L^p$ (not using interpolation), and there is a good reason to do so when a sharp bound for the operator norm is desired. See, for example, The Hunt for a Bellman function by Nazarov and Treil.

share|cite|improve this answer

Your Answer


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

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