Abstract
Let Hn be the (2n+1)-dimensional Heisenberg group. We consider a radial Fourier multiplier which is a spherical function on Hn and show that it is a Herz-Schur multiplier.
Highlights
The Theory of multipliers has grown over the years to yield several results and applications in virtually all aspects of Analysis and Mathematics in general
We consider a radial Fourier multiplier which is a spherical function on IHn and show that it is a Herz-Schur multiplier
A transference result of Fourier multipliers from SU (2) to the Heisenberg group was considered by F.Ricci [15]
Summary
The Theory of multipliers has grown over the years to yield several results and applications in virtually all aspects of Analysis and Mathematics in general. The theory was introduced on the Heisenberg group by G. A transference result of Fourier multipliers from SU (2) to the Heisenberg group was considered by F.Ricci [15]. The spherical functions form a large subject matter on this group [3], [1]. A construction of spherical radial functions on the Heisenberg group was given in [5], [6] and [7]. The concept of Schur multipliers or completely bounded functions has attained an exciting peak in Harmonic Analysis. Key words and phrases. spherical-radial multipliers; Herz-Schur; Heisenberg group
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