Rectangular Summation of Multiple Fourier Series and Multi-parametric Capacity
Rectangular Summation of Multiple Fourier Series and Multi-parametric Capacity
Abstract We consider the class of multiple Fourier series associated with functions in the Dirichlet space of the polydisc. We prove that every such series is summable with respect to unrestricted rectangular partial sums, everywhere except for a set of zero multi-parametric logarithmic capacity. Conversely, given a compact set in …