Generalized Multiple Multiplicative Fourier Transform and Estimates of Integral Moduli of Continuity

The paper presents the properties of generalized multiple multiplicative Fourier transforms. Also, upper and lower bounds are given for the integral modulus of continuity in terms of the mentioned Fourier transforms, and the bound in $L^2$ is unimprovable. As a corollary, an analogue of Titchmarsh's equivalence theorem for the multiplicative Fourier transform is obtained.