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Analysis of PDEsmathscidoc: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.
@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.