School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332-0160
Abstract:
In his fundamental research on generalized harmonic analysis, Wiener proved that the integrated Fourier transform defined by is an isometry from a nonlinear space of functions of bounded average quadratic power into a nonlinear space of functions of bounded quadratic variation. We consider this Wiener transform on the larger, linear, Besicovitch spaces defined by the norm . We prove that maps continuously into the homogeneous Besov space for and , and is a topological isomorphism when .