Function Spaces and Their Operators
A Conference in Honor of Richard Rochberg on the Occasion of his 65th Birthday

Tadeusz Iwaniec from Syracuse University; From Coifman-Rochberg-Weiss Commutators through Jacobians and Null Lagrangians to Nonlinear Hyperelasticity; May 29, 2008.

Abstract: This lecture features new types of maximal functions and commutators of singular integrals, linear and nonlinear. The topics are motivated by the study of nonlinear differential expressions which arise naturally in geometric function theory, nonconvex calculus of variations and nonlinear elasticity. In particular, estimates of the Jacobian determinant in the Hardy space by means of subdeterminants involves an interpolation between maximal avarages over the balls (Hardy maximal function) and spherical maximal avarages (Fefferman-Stein maximal operator).