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

Resumo

We consider a new class of functions on the p-adic linear space ℚ_pⁿ 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 L²(ℚ_pⁿ) 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_pⁿ) with appropriate q.