On the Carleson duality |
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Authors: | Tuomas Hytönen Andreas Rosén |
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Institution: | 1. Department of Mathematics and Statistics, P.O. Box 68 (Gustaf H?llstr?ms gata 2b), FI-00014, Helsingfors universitet, Finland 2. Department of Mathematics, Link?pings universitet, SE-581 83, Link?ping, Sweden
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Abstract: | As a tool for solving the Neumann problem for divergence-form equations, Kenig and Pipher introduced the space ${\mathcal{X}}$ of functions on the half-space, such that the non-tangential maximal function of their L 2 Whitney averages belongs to L 2 on the boundary. In this paper, answering questions which arose from recent studies of boundary value problems by Auscher and the second author, we find the pre-dual of ${\mathcal{X}}$ , and characterize the pointwise multipliers from ${\mathcal{X}}$ to L 2 on the half-space as the well-known Carleson-type space of functions introduced by Dahlberg. We also extend these results to L p generalizations of the space ${\mathcal{X}}$ . Our results elaborate on the well-known duality between Carleson measures and non-tangential maximal functions. |
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