VOLTER CONVOLUTION OPERATORS IN HÖLDER SPACES

The monograph studies mixed integrals of Voltaire convolution type operators of two variables in generalized Gelder spaces of different orders on each variable, defined by a mixed continuity module. We consider Gelder spaces defined both by first-order differences of different orders on each variable and by mixed second-order differences, the main interest being the evaluation of the latter for the mixed fractional integral in both cases when the density of the integral belongs to the Gelder class of those defined by ordinary or mixed differences.