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On the Carleson duality
University of Helsinki, Finland.
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
2013 (English)In: Arkiv för matematik, ISSN 0004-2080, E-ISSN 1871-2487, Vol. 51, no 2, 293-313 p.Article in journal (Refereed) Published
Abstract [en]

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 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 X , and characterize the pointwise multipliers from 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 X . Our results elaborate on the well-known duality between Carleson measures and non-tangential maximal functions.

Place, publisher, year, edition, pages
Springer Netherlands, 2013. Vol. 51, no 2, 293-313 p.
National Category
Mathematical Analysis
URN: urn:nbn:se:liu:diva-89294DOI: 10.1007/s11512-012-0167-7ISI: 000323247000005OAI: diva2:607644
Available from: 2013-02-25 Created: 2013-02-25 Last updated: 2013-09-06Bibliographically approved

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