On trigonometric polynomials (Q1909788)

The function \(F: \mathbb{R}\to \mathbb{R}\), local integrable on the whole axis, generates the following trigonometric integral \(I(f; x):= \int_\mathbb{R} F(t) \exp (itx) dt\), \(x\in \mathbb{R}\). The main purpose of this paper is to establish sufficient conditions such that \(I(f; x)\in L_p [ a,b ]\), \(1\leq p\), \(-\infty< a< b< \infty\).