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On the Dirichlet space for finitely connected regions

1990
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Transactions of the American Mathematical Society
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This paper is devoted to the study of the Dirichlet space Dir(G) for finitely connected regions G ; we are particularly interested in the algebra of bounded multiplication operators on this space. Results in different directions are obtained. One direction deals with the structure of closed subspaces invariant under all bounded multiplication operators. In particular, we show that each such subspace contains a bounded function. For regions with circular boundaries we prove that a finite

doi:10.1090/s0002-9947-1990-0958885-4
fatcat:hh3dizjz7nebne3anzlhry3yni