On Littlewood-Paley functions

Cheng, Leslie

doi:10.1090/S0002-9939-07-08917-4

On Littlewood-Paley functions
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by Leslie C. Cheng

Proc. Amer. Math. Soc. 135 (2007), 3241-3247

DOI: https://doi.org/10.1090/S0002-9939-07-08917-4

Published electronically: June 20, 2007

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Abstract:

We prove that, for a compactly supported $L^q$ function $\Phi$ with vanishing integral on $\mathbf {R}^n$, the corresponding square function operator $S_\Phi$ is bounded on $L^p$ for $|1/p - 1/2| < \min \{(q-1)/2, 1/2\}$.

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