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Some orthogonal decompositions of Sobolev spaces and applications

H. BegehrYu. Dubinskiĭ — 2001

Colloquium Mathematicae

Two kinds of orthogonal decompositions of the Sobolev space W̊₂¹ and hence also of W - 1 for bounded domains are given. They originate from a decomposition of W̊₂¹ into the orthogonal sum of the subspace of the Δ k -solenoidal functions, k ≥ 1, and its explicitly given orthogonal complement. This decomposition is developed in the real as well as in the complex case. For the solenoidal subspace (k = 0) the decomposition appears in a little different form. In the second kind decomposition the Δ k -solenoidal...

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