Some New Estimates of the Fourier Transform in L2(R)

Given a function L-2(R), its Fourier transform g(x) = (f) over cap (x) = F[f](x) = 1/root 2 pi(+infinity)(-infinity)integral f(x)e(-ixt)dt, f(t) = F-1[g](t) = 1/root 2 pi(+infinity)(-infinity)integral g(x)e(ixt)dx and the inverse Fourier transform are considered in the space f is an element of L-2(R). New estimates are presented for the integral integral(vertical bar t vertical bar >= N) vertical bar g(l)vertical bar(2)dl = integral(vertical bar t vertical bar >= N)vertical bar(integral) over cap (l)vertical bar(2)dl, N >= 1, in the vase of f is an element of L-2(R) characterized by the generalized modulus of continuity of the kth order constructed with the help of the Steklov function. Some other estimates associated with this integral are proved.