Boundedness and compactness of Heckman–Opdam two-wavelet multipliers

Abstract

We introduce the notion of a Heckman–Opdam two-wavelet multiplier, and give a trace formula for a Heckman–Opdam two-wavelet multiplier as a bounded linear operator in the trace class from \(L^{2}_{A_{k}}(\mathbb {R}^{d})\) into \(L^{2}_{A_{k}}(\mathbb {R}^{d})\) in terms of the symbol and the two admissible wavelets. Next, we give results on the boundedness and compactness of two Heckman–Opdam wavelet multipliers on \(L^{p}_{A_{k}}(\mathbb {R}^{d})\), \(1 \le p \le \infty \).