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$L^1$ maximal regularity for the laplacian and applications
Inter alia we prove $L^1$ maximal regularity for the Laplacian in the
space of Fourier transformed nite Radon measures FM. This is remarkable,
since FM is not a UMD space and by the fact that we obtain $L_p$ maximal
regularity for $p$ = 1, which is not even true for the Laplacian in $L^2$. We apply
our result in order to construct strong solutions to the Navier-Stokes equations
for initial data in FM in a rotating frame. In particular, the obtained results
are uniform in the angular velocity of rotation.