Boundedness of the orthogonal projection on Harmonic Fock spaces
The main result of this paper refers to the boundedness of the orthogonal projection $P_α:L^{2}(\mathbb{R}^{n},dμ_α)\rightarrow \mathcal{H}_α^{2}, n\geq2 $ associated to the harmonic Fock space $\mathcal{H}_α^{2},$ where $dμ_α(x)=(πα)^{-n/2}e^{-\frac{|x|^2}α}dx.$ We prove that the operator $P_α$ is not bounded on $L^{p}(\mathbb{R}^{n},dμ_β)$ when $0<p< 1$ and we found a necessary and sufficient condition for the boundedness when $1\leq p<\infty$ and $n$ is an even integer.
math.FA↗