Spherical Fourier multipliers related to Gelfand pairs

Abstract: In this paper, we introduce a family of Fourier multipliers using the spherical Fourier transform on Gelfand pairs. We refer to them as spherical Fourier multipliers. We study certain sufficient conditions under which they are bounded. Then, under the hypothesis of compactness of the underlying group and under certain summability conditions, we obtain the belonging of the spherical Fourier multipliers to some Schatten-von Neumann classes.