MathOverflow is a question and answer site for professional mathematicians. 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 famous result is that $H^p\cap L^1$ is a dense subspace of $H^p$. We need the fact that $\displaystyle\sup_{0<s\leq M}|(P_s*P_t*f-P_s*f)(x)|$, where $P_t$ is the Poisson kernel on $R^n$ and $f\in H^p$ and $x$ is fixed, is continuous for $t\in[0,1)$ to prove it, but I don't know how can we prove the continuity of this function. Or is there somebody who can tell me who is the first person proved the density( maybe by different method)?

share|cite|improve this question
What exactly is $H^p$ here? – Nate Eldredge Aug 29 '12 at 3:32
It means the Harday spaces: bounded distribution $f$ s.t. $\sup_{s>0}|(P_s*f)(x)|\in L^p$ – Danqing Aug 29 '12 at 3:57

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.