Abstract
We extend the recently developed L p -theory for the maximal regularity of the abstract Cauchy problem $$ [\ifmmode\expandafter\dot\else\expandafter\.\fi{u} + Au = f,u(0) = 0] $$ and the related Fourier multiplier techniques to the real-variable Hardy space H1. Some results for H p , 0 < p < 1, are also proved.
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