Sharp weak bounds for the Hardy-Littlewood-Pólya operator and the weak bounds for the multilinear integral operator

2025/05/23 by He, Tianyang
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2505.17707

Abstract

In this paper, we first obtain the operator norms of the n-dimensional Hardy-Littlewood-Pólya operator H from weighted Lebesgue spaces L^p( ℝ ⁿ,| x |^β ) to weighted weak Lebesgue spaces L^q,∞(ℝ ⁿ,|x|^γ). Next, we obtain the weak bounds for the m-linear n-dimensional integral operator.

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