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A continuous characterization of Triebel-Lizorkin spaces associated with Hermite expansions. (English) Zbl 1330.46032

The well-known spaces \(F^s_{p,q}\) in \(\mathbb R^n\) with \(s\in \mathbb R\), \(0<p<\infty\), \(0<q \leq \infty\) can be characterized in terms of spectral decompositions of the Laplace operator \(-\Delta\). If one replaces \(-\Delta\) by the Hermite operator \(D = -\Delta + |x|^2\) then one obtains related spaces \(F^s_{p,q} (D)\). The paper contributes to the corresponding theory.

MSC:

46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
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