## Arkiv för Matematik

• Ark. Mat.
• Volume 51, Number 2 (2013), 293-313.

### On the Carleson duality

#### 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 L2 Whitney averages belongs to L2 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 L2 on the half-space as the well-known Carleson-type space of functions introduced by Dahlberg. We also extend these results to Lp generalizations of the space ${\mathcal{X}}$. Our results elaborate on the well-known duality between Carleson measures and non-tangential maximal functions.

#### Note

Andreas Rosén was earlier named Andreas Axelsson.

#### Article information

Source
Ark. Mat., Volume 51, Number 2 (2013), 293-313.

Dates
First available in Project Euclid: 1 February 2017

https://projecteuclid.org/euclid.afm/1485907215

Digital Object Identifier
doi:10.1007/s11512-012-0167-7

Mathematical Reviews number (MathSciNet)
MR3090198

Zentralblatt MATH identifier
1294.42002

Rights

#### Citation

Hytönen, Tuomas; Rosén, Andreas. On the Carleson duality. Ark. Mat. 51 (2013), no. 2, 293--313. doi:10.1007/s11512-012-0167-7. https://projecteuclid.org/euclid.afm/1485907215

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