This transform was at the time the subject of a conjecture by Alberto Calderón that Lacey and Christoph Thiele solved in 1996, for which they were awarded the Salem Prize.
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.
He was on the 1980s CBS series Cagney & Lacey as Michael Lacey, one of the on-screen children of Mary Beth Lacey (Tyne Daly) and Harvey Lacey Sr.