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arXiv · 1902.08417

Boundedness of the orthogonal projection on Harmonic Fock spaces

Djordjije Vujadinović
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Abstract

The main result of this paper refers to the boundedness of the orthogonal projection $P_{\alpha}:L^{2}(\mathbb{R}^{n},d\mu_{\alpha})\rightarrow \mathcal{H}_{\alpha}^{2}, n\geq2 $ associated to the harmonic Fock space $\mathcal{H}_{\alpha}^{2},$ where $d\mu_{\alpha}(x)=(\pi\alpha)^{-n/2}e^{-\frac{|x|^2}{\alpha}}dx.$ We prove that the operator $P_{\alpha}$ is not bounded on $L^{p}(\mathbb{R}^{n},d\mu_{\beta})$ 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.

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Djordjije Vujadinović. 2019-02-22. Boundedness of the orthogonal projection on Harmonic Fock spaces. https://arxiv.org/abs/1902.08417

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