This is an announcement for the paper "$L^\infty$ to $L^p$ constants for Riesz projections" by Jordi Marzo and Kristian Seip.
Abstract: The norm of the Riesz projection from $L^\infty(\T^n)$ to $L^p(\T^n)$ is considered. It is shown that for $n=1$, the norm equals $1$ if and only if $p\le 4$ and that the norm behaves asymptotically as $p/(\pi e)$ when $p\to \infty$. The critical exponent $p_n$ is the supremum of those $p$ for which the norm equals $1$. It is proved that $2+2/(2^n-1)\le p_n <4$ for $n>1$; it is unknown whether the critical exponent for $n=\infty$ exceeds $2$.
Archive classification: math.FA math.CV
Mathematics Subject Classification: 41A44, 42B05, 46E30
Submitted from: seip@math.ntnu.no
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1005.1842
or