Fock projections on vector-valued L^p-spaces with matrix weights

2024/08/24 by Chen, Jiale, Wang, Maofa
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2408.13537

Abstract

In this paper, we characterize the d× d matrix weights W on ℂⁿ such that the Fock projection P_α is bounded on the vector-valued spaces L^p_α,W(ℂⁿ;ℂ^d) induced by W and the Gaussian measures. It is proved that for 1≤ p≤∞, the Fock projection P_α is bounded on L^p_α,W(ℂⁿ;ℂ^d) if and only if W satisfies a restricted A_p-condition. Our result is new even in the scalar setting at the endpoint p=∞.

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