Generalized p-Adic Fourier Transform and Estimates of Integral Modulus of Continuity in Terms of This Transform

We consider a new class of functions on the p-adic linear space Q(p)(n) for which a Fourier transform can be defined. We prove equalities of Parseval type, an inversion formula and a sufficient condition for a function to be represented as this Fourier transform. Also we give a sharp estimate of the L-2(Q(p)(n)) modulus of continuity in terms of Fourier transform generalizing the result of S. S. Platonov in the case n = 1. Finally we prove a generalization of this result and its converse for L-q(Q(p)(n)) with appropriate q.