On the Carleson duality

Tuomas Hytönen Department of Mathematics and Statistics, P.O. Box 68 (Gustaf Hällströms gata 2b), Helsingfors universitet, Finland Andreas Rosén Department of Mathematics, Linköpings universitet

Analysis of PDEs mathscidoc:1701.03025

Arkiv for Matematik, 51, (2), 293-313, 2011.4
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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@inproceedings{tuomas2011on,
  title={On the Carleson duality},
  author={Tuomas Hytönen, and Andreas Rosén},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203635314713042},
  booktitle={Arkiv for Matematik},
  volume={51},
  number={2},
  pages={293-313},
  year={2011},
}
Tuomas Hytönen, and Andreas Rosén. On the Carleson duality. 2011. Vol. 51. In Arkiv for Matematik. pp.293-313. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203635314713042.
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