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arXiv · 1104.1960

On the Carleson duality

Tuomas Hytönen·Andreas Rosén
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Abstract

As a tool for solving the Neumann problem for divergence form equations, Kenig and Pipher introduced the space 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 X, and characterize the pointwise multipliers from 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 X. Our results elaborate on the well-known duality between Carleson measures and non-tangential maximal functions.

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Tuomas Hytönen, Andreas Rosén. 2011-04-11. On the Carleson duality. https://doi.org/10.1007/s11512-012-0167-7

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