An analysis of a wide class of integral transforms with product kernels from the two-weighted boundedness point of view. This book discusses weighted integral in-equalities for monotonic functions of several variables.

The classical theory of Fourier series deals with decomposition of a function into sinusoidal waves. Unlike these continuous waves the Vilenkin (Walsh) functions are rectangular waves. Such waves have already been used frequently in the theory of signal transmission, multiplexing, filtering, image enhancement, code theory, digital signal processing and pattern recognition. The development of the theory of Vilenkin-Fourier series has been...