This is an announcement for the paper "Haar projection numbers and failure of unconditional convergence in Sobolev spaces" by Andreas Seeger and Tino Ullrich.

Abstract: For $1<p<\infty$ we determine the precise range of $L_p$ Sobolev spaces for which the Haar system is an unconditional basis. We also consider the natural extensions to Triebel-Lizorkin spaces and prove upper and lower bounds for norms of projection operators depending on properties of the Haar frequency set.

Archive classification: math.CA math.FA

Mathematics Subject Classification: 46E35, 46B15, 42C40

Submitted from: seeger@math.wisc.edu

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1507.01211

or

http://arXiv.org/abs/1507.01211