Poisson integrals and Riesz transforms for Hermite function expansions with weights

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Besov and Triebel-Lizorkin Spaces Associated to Hermite Operators (2015, background): “See for example [14,15].”
Fractional powers of second order partial differential operators: extension problem and regularity theory (2010, methodology): “By writing down the integral in ⟨f,hν⟩ and applying Fubini's Theorem, the heat semigroup can be given as an integral operator, and the formula extends to f ∈ ∪ 16p6∞pn (see also [78]): ef(x) = ∫ Rn Gt(x, z)f(z) dz”