A continuous characterization of Triebel-Lizorkin spaces associated with Hermite expansions (Q492487)

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.