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Search: MSC category 47D06
( Oneparameter semigroups and linear evolution equations [See also 34G10, 34K30] )
1. CJM Online first
 Graczyk, Piotr; Kemp, Todd; Loeb, JeanJacques

Strong Logarithmic Sobolev Inequalities for LogSubharmonic Functions
We prove an intrinsic equivalence between strong
hypercontractivity and a strong logarithmic Sobolev
inequality for the cone of logarithmically subharmonic
(LSH) functions. We introduce a new large class of measures,
Euclidean regular and exponential type, in addition to all compactlysupported
measures, for which this equivalence holds. We prove a Sobolev
density theorem through LSH functions and use it to prove
the equivalence of strong
hypercontractivity and the strong logarithmic Sobolev
inequality for such logsubharmonic
functions.
Keywords:logarithmic Sobolev inequalities Category:47D06 

2. CJM 2007 (vol 59 pp. 1207)
 Bu, Shangquan; Le, Christian

$H^p$Maximal Regularity and Operator Valued Multipliers on Hardy Spaces
We consider maximal regularity in the $H^p$ sense for the Cauchy
problem $u'(t) + Au(t) = f(t)\ (t\in \R)$, where $A$ is a closed
operator on a Banach space $X$ and $f$ is an $X$valued function
defined on $\R$. We prove that if $X$ is an AUMD Banach space,
then $A$ satisfies $H^p$maximal regularity if and only if $A$ is
Rademacher sectorial of type $<\frac{\pi}{2}$. Moreover we find an
operator $A$ with $H^p$maximal regularity that does not have the
classical $L^p$maximal regularity. We prove a related Mikhlin
type theorem for operator valued Fourier multipliers on Hardy
spaces $H^p(\R;X)$, in the case when $X$ is an AUMD Banach space.
Keywords:$L^p$maximal regularity, $H^p$maximal regularity, Rademacher boundedness Categories:42B30, 47D06 
