Professor Asmar's research project concerns the applications of transference methods in analysis. The emphasis is on finding dimension independent bounds on the strong and weak type norms of maximal operators and other singular integral operators. The method and applications under study involve the kinds of operators or functions in infinite dimensional spaces which occur in the analysis of the partial differential equations of mathematical physics. This includes, for example, the equations of electromagnetism and fluid dynamics. Knowing that these are bounded operators is often an important first step in studying solutions to these equations.
