Growth estimates for the singular values of square-integrable kernels

This paper is concerned with the unique correspondences which exist between the values of convergence exponents for the classical Fourier coefficients of one-variable functions satisfying various smoothness assumptions, on the one hand, and growth estimates for the singular values n associated with square-integrable two-variable kernels K(x, y), a^x, y = fc, having comparable smoothness, on the other. Extending earlier work of the author and others, precise values are given for the infimum of for which (l/ n )