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M. Oliver,
An estimate on the Bedrosian commutator in Sobolev space,
J. Inequal. Appl. 2018 (2018), 348, doi:10.1186/s13660-018-1940-3.
Abstract:
While the Bedrosian identity for the Hilbert transform of a product
does not hold for general Sobolev class functions, we show that the
defect of this identity is more regular than would be naively
expected. We use this result to give a stronger-than-expected
estimate on the chain rule defect of the square root of the Laplacian.
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