Haar projection numbers and failure of unconditional convergence in Sobolev spaces
classification
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haarspacesprojectionsobolevunconditionalbasisboundsconsider
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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.
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