Specializing in harmonic analysis and operator theory, he is mostly known for, together with Steve Hofmann, Michael Lacey, Alan McIntosh and Philippe Tchamitchian, solving the famous Kato's conjecture.
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The problem remained unresolved for nearly a half-century, until it was jointly solved in 2001 by Pascal Auscher, Steve Hofmann, Michael Lacey, Alan McIntosh, and Philippe Tchamitchian.