An estimate on the Bedrosian commutator in Sobolev space

Abstract

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.

Keywords

• Bedrosian identity
• Sobolev space
• Banach algebra