Resumen de The sets of convergence in measure of multiple orthogonal Fourier series

Rostom Getsadze

• Let be an arbitrary orthonormal system on [0,1] that is uniformly bounded by a constant . Let be a subset of [0,1] such that the Fourier series of all Lebesgue integrable functions on [0,1] with respect to the product system converge in measure by squares on . The following problem is studied. How large may the measure of be? A theorem is proved that implies that for each such system, there is (for the -fold product systems, ). This estimate is sharp in the class of all such product systems.