Characterizations of Hankel multipliers

Abstract

We give characterizations of radial Fourier multipliers as acting on radial L p functions, 1 < p < 2d/(d + 1), in terms of Lebesgue space norms for Fourier localized pieces of the convolution kernel. This is a special case of corresponding results for general Hankel multipliers. Besides L p − L q bounds we also characte- rize weak type inequalities and intermediate inequalities involving Lorentz spaces. Applications include results on interpolation of multiplier spaces.