We extend the recently developed
Lp-theory for the maximal regularity of the abstract Cauchy problem
$
[\ifmmode\expandafter\dot\else\expandafter\.\fi{u} + Au = f,u(0) = 0]
$
[\ifmmode\expandafter\dot\else\expandafter\.\fi{u} + Au = f,u(0) = 0]
and the related Fourier multiplier techniques to the real-variable Hardy space
H1. Some results for
Hp, 0 <>
p < 1,="" are="" also="">
Mathematics Subject Classification (2000). Primary 34G10 - Secondary 42B30
Key words. Hardy spaces of vector-valued functions - operator-valued Fourier multipliers - abstract Cauchy problem - maximal regularity