Boundedness and compactness of Heckman–Opdam two-wavelet multipliers

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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 \(L^{p}_{A_{k}}(\mathbb {R}^{d})\), \(1 \le p \le \infty \).

Keywords

Hypergeometric Fourier transform Heckman–Opdam multipliers Heckman–Opdam two-wavelet multipliers Schatten–von Neumann class 

Mathematics Subject Classification

Primary 44A05 Secondary 42B10 
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Notes

Acknowledgements

The author is deeply indebted to the referees for providing constructive comments and helps in improving the contents of this article.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Mathematics, College of SciencesTaibah UniversityAl Madinah AL MunawarahSaudi Arabia

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