Boundedness of the Segal-Bargmann transform on fractional Hermite-Sobolev spaces. (English) Zbl 1377.46023
Summary: Let \(s \in \mathbb{R}\) and \(2 \leq p \leq \infty\). We prove that the Segal-Bargmann transform \(\mathcal{B}\) is a bounded operator from fractional Hermite-Sobolev spaces \(W_H^{s, p} \left(\mathbb{R}^n\right)\) to fractional Fock-Sobolev spaces \(F_{\mathcal{R}}^{s, p}\).
MSC:
| 46E35 | Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems |
References:
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