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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.
In mathematics, in the area of functional analysis and operator theory, the Volterra operator, named after Vito Volterra, represents the operation of indefinite integration, viewed as a bounded linear operator on the space L2(0,1) of complex-valued square integrable functions on the interval (0,1).
Resolvent set in operator theory, the set of points where an operator is "well-behaved"