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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Andreas Rosén was earlier named Andreas Axelsson.
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Hytönen, T., Rosén, A. On the Carleson duality. Ark Mat 51, 293–313 (2013). https://doi.org/10.1007/s11512-012-0167-7
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DOI: https://doi.org/10.1007/s11512-012-0167-7