… In this article we describe a new characterization of maximal Lp-regularity for the Cauchy
problem of semigroup generators in terms of square function estimates, or more generally in
terms of β -boundedness (see Section 1). In Section 2 we use Fourier multiplier theorems for
operator-valued multiplier functions as in [50], in Section 3 we give a second proof using a … c)
Examples There is a rich literature on sufficient conditions for maximal Lpregularity, which
implies that most classical differential operators that may be of interest in the problems just …