155 research outputs found
Real interpolation of Sobolev spaces
We prove that is an interpolation space between
and for and on some
classes of manifolds and general metric spaces, where depends on our
hypotheses.Comment: 30 page
Interpolation, embeddings and traces of anisotropic fractional Sobolev spaces with temporal weights
We investigate the properties of a class of weighted vector-valued
-spaces and the corresponding (an)isotropic Sobolev-Slobodetskii spaces.
These spaces arise naturally in the context of maximal -regularity for
parabolic initial-boundary value problems. Our main tools are operators with a
bounded \calH^\infty-calculus, interpolation theory, and operator sums.Comment: This is a preprint version. Published in Journal of Functional
Analysis 262 (2012) 1200-122
Real Interpolation method, Lorentz spaces and refined Sobolev inequalities
In this article we give a straightforward proof of refined inequalities
between Lorentz spaces and Besov spaces and we generalize previous results of
H. Bahouri and A. Cohen. Our approach is based in the characterization of
Lorentz spaces as real interpolation spaces. We will also study the sharpness
and optimality of these inequalities
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