Lebesgue bounds for multilinear spherical and lacunary maximal averages

2024/11/18 by Gao, Xinyu · 1 citation
Decision Sciences · Mathematics · #Advanced Banach Space Theory #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Point processes and geometric inequalities #Risk and Portfolio Optimization

paper · pdf · doi:10.48550/arxiv.2411.11255

openalex publication_date 2024/11/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish L^p₁(\mathbb R^d) × ⋯ × L^p_n(\mathbb R^d) → L^r(\mathbb R^d) bounds for spherical averaging operators \mathcal Aⁿ in dimensions d ≥ 2 for indices 1≤ p₁,… , p_n≤ ∞ and (1)/(p₁)+⋯ +(1)/(p_n)=(1)/(r). We obtain this result by first showing that \mathcal Aⁿ maps L¹ × ⋯ × L¹ → L¹. We also obtain similar estimates for lacunary maximal spherical averages in the largest possible open region of indices.

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• Bilinear spherical maximal function with fractal dilations

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