to ensure that f belongs to one of the Lipschitz classes Lip α and lip α for some 0 < α ≤ 1, or to one of the Zygmund classes Zyg α and zyg α for some 0 < α ≤ 2. The conditions given by us are not only sufficient, but also necessary in the case when the sine and cosine transforms
are nonnegative. Our theorems are extensions of the corresponding theorems by Boas from sine and cosine series to sine and
We investigate the pointwise and uniform convergence of the symmetric rectangular partial (also called Dirichlet) integrals of the double Fourier integral of a function that is Lebesgue integrable and of bounded variation over ℝ2. Our theorem is a two-dimensional extension of a theorem of Móricz (see Theorem 3 in ) concerning the single Fourier integrals, which is more general than the two-dimensional extension given by Móricz himself (see Theorem 3 in ).