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HILBERT TRANSFORMS ALONG LIPSCHITZ DIRECTION FIELDS: A LACUNARY MODEL
Published online by Cambridge University Press: 09 February 2017
Abstract
We prove bounds for the truncated directional Hilbert transform in $L^{p}(\mathbb{R}^{2})$ for any $1<p<\infty$ under a combination of a Lipschitz assumption and a lacunarity assumption. It is known that a lacunarity assumption alone is not sufficient to yield boundedness for $p=2$, and it is a major question in the field whether a Lipschitz assumption alone suffices, at least for some $p$.
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- Copyright © University College London 2017
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