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HILBERT TRANSFORMS ALONG LIPSCHITZ DIRECTION FIELDS: A LACUNARY MODEL

  • Shaoming Guo (a1) (a2) and Christoph Thiele (a3)

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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Mathematika
  • ISSN: 0025-5793
  • EISSN: 2041-7942
  • URL: /core/journals/mathematika
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