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Journal of Fourier Analysis and Applications

, Volume 25, Issue 6, pp 2877–2898 | Cite as

The Stability of Wavelet-Like Expansions in \(A_\infty \) Weighted Spaces

  • Michael WilsonEmail author
Article

Abstract

We prove \(L^p\) boundedness in \(A_\infty \) weighted spaces for operators defined by almost-orthogonal expansions indexed over the dyadic cubes. The constituent functions in the almost-orthogonal families satisfy weak decay, smoothness, and cancellation conditions. We prove that these expansions are stable (with respect to the \(L^p\) operator norm) when the constituent functions suffer small dilation and translation errors.

Keywords

Littlewood–Paley theory Almost-orthogonality Weighted norm inequality Bounded mean oscillation Singular integral operators 

Mathematics Subject Classification

42B25 primary 42B20 secondary 

Notes

Acknowledgements

The author is glad to express his deep gratitude to the anonymous referees, whose careful reading spotted many typographical errors, and whose detailed and insightful comments on style and structure greatly improved the paper’s readability. Also, thanks to them, the author has begun to think about this work, and its relation to other results, in ways that had not occurred to him before. Thank you!

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of VermontBurlingtonUSA

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