Weyl transforms associated with the spherical mean operator. (English) Zbl 1045.47038
Summary: Using the harmonic analysis associated with the spherical mean operator \(\mathcal R\), we define and study the Weyl transforms \(W_{\sigma}\) associated with \(\mathcal R\) where \(\sigma\) is a symbol in \(S^m\), \(m \in \mathbb R\), and we give criteria in terms of \(\sigma\) to obtain the boundedness and compactness of the transform \(W_{\sigma}\).
MSC:
| 47G10 | Integral operators |
| 43A32 | Other transforms and operators of Fourier type |
| 44A15 | Special integral transforms (Legendre, Hilbert, etc.) |
References:
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