On some sufficient conditions for Fourier multipliers and absolute convergence of the Fourier transform

Mon, 24/02/2014 - 15:05

We present new sufficient conditions for Fourier multipliers. These conditions are given in terms of simultaneous
behavior of (quasi-)norms of a function in different Lebesgue and Besov spaces. We also provide some sufficient
conditions for the representation of a function as an absolute convergence Fourier integrals in terms of belonging
of a function simultaneously to several spaces of smooth functions.