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On the Almost Everywhere Convergence of Wavelet Summation Methods

✍ Scribed by Terence Tao

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 124 KB
Volume: 3
Category: Article
ISSN: 1063-5203
DOI: 10.1006/acha.1996.0031

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✦ Synopsis

Let ψ be a rapidly decreasing one-dimensional wavelet. We show that the wavelet expansion of any L p function converges pointwise almost everywhere under the wavelet projection, hard sampling, and soft sampling summation methods, for 1 < p < ∞. In fact, the partial sums are uniformly dominated by the Hardy-Littlewood maximal function.

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