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Much of this paper will be concerned with the proof of the following
Theorem 1. Suppose d ≥ 3, r = max {d, (3d - 4)/2}. If V ∈ Lloc
r(Rd), then the differential inequality |Δu| ≤ V |∇u| has the strong unique continuation property in the following sense: If u belongs to the Sobolev space Wloc
2,p and if |Δu| ≤ V |∇u| and
...
Let , denote the space of Bessel potentials , , with norm . For integer can be identified with the Sobolev space .
One can associate a potential theory to these spaces much in the same way as classical potential theory is associated to the space , and a considerable part of the theory was carried over to this more general context around 1970. There were difficulties extending the theory of thin sets, however. By means of a new inequality, which characterizes the positive cone...
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