Fourier Multipliers in Hardy Spaces in Tubes over Open Cones

We obtain effective sufficient conditions for multipliers of Fourier integrals acting from H-p (T-Gamma) to H-q (T-Gamma), 0 < p <= q <= 1. We also show that they are sharp in some cases. Special attention is paid to the means of Fourier integrals with compactly supported radial kernels. As an application, the critical index for the Bochner-Riesz means to define a bounded linear operator from H-p to H-q is found. Surprisingly, it does not depend on p.