Invariance and stability of almost-orthogonal systems

Author:
Michael Wilson

Journal:
Trans. Amer. Math. Soc. **368** (2016), 2515-2546

MSC (2010):
Primary 42B25; Secondary 42B20

Published electronically:
August 18, 2015

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Abstract: For , let be the uniformly (norm ) -Hölder continuous functions with supports contained in the unit ball of . Let be any family indexed over the dyadic cubes . If is the center of and is its sidelength, we define , and we set:

is almost-orthogonal in ; where we say a family is almost-orthogonal in if there is an such that, for all finite subsets and all linear sums ,

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Additional Information

**Michael Wilson**

Affiliation:
Department of Mathematics, University of Vermont, Burlington, Vermont 05405

DOI:
https://doi.org/10.1090/tran/6433

Keywords:
Littlewood-Paley theory,
almost-orthogonality,
weighted norm inequality,
bounded mean oscillation,
singular integral operators

Received by editor(s):
February 4, 2013

Received by editor(s) in revised form:
January 21, 2014

Published electronically:
August 18, 2015

Article copyright:
© Copyright 2015
American Mathematical Society