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REAL INTERPOLATION OF SOBOLEV SPACES

NADINE BADR
Mathematica Scandinavica
Vol. 105, No. 2 (2009), pp. 235-264
Published by: Mathematica Scandinavica
Stable URL: http://www.jstor.org/stable/24493650
Page Count: 30
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
REAL INTERPOLATION OF SOBOLEV SPACES
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Abstract

We prove that ${\mathrm{W}}_{\mathrm{p}}^{1}$ is a real interpolation space between ${\mathrm{W}}_{{\mathrm{p}}_{1}}^{1}$ and ${\mathrm{W}}_{{\mathrm{p}}_{2}}^{1}$ for p > q0 and 1 ≤ p1 < p < p2 ≤ ∞ on some classes of manifolds and general metric spaces, where q0 depends on our hypotheses.

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