Boundedness and compactness of Heckman-Opdam two-wavelet multipliers
The behavior of hypergeometric Fourier transform has been investigated by several authors to solve the problems of wavelet theory, real Paley-Wiener theorems, uncertanity principles and so on. Using the properties of hypergeometric Fourier transform the two wavelet multipliers associated to Heckman-Opdam theory have been exposed and studied in this paper. The wavelet multipliers were introduced by \textit{Z. He} and \textit{M. W. Wong} [J. Aust. Math. Soc., Ser. B 40, No. 4, 437--446 (1999; Zbl 0937.35196)] and detailed in the book [Wavelet transforms and localization operators. Basel: Birkhäuser (2002; Zbl 1016.42017)] by \textit{M.-W. Wong}. The results studied in this paper generalized the various results of \textit{M. W. Wong} and \textit{Z. Zhang} [Integral Equations Oper. Theory 42, No. 4, 498--503 (2002; Zbl 1021.42018); Bull. Lond. Math. Soc. 34, No. 6, 739--744 (2002; Zbl 1048.47037)]. Moreover, the Schatten-von Neumann properties of above mentioned wavelet multipliers have been established. Also, the \(L^{p}\)-boundedness and compactness with the traces and trace class norm inequalities have been obtained.
scientific article; zbMATH DE number 6818234
scientific article