Fractional integrals associated with Zygmund dilations

2025/04/12 by Zipeng Wang, Wang, Zipeng
Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Fractional Differential Equations Solutions #Mathematical functions and polynomials #Nonlinear Differential Equations Analysis

paper · pdf · doi:10.48550/arxiv.2504.09092

openalex publication_date 2025/04/12 · openalex created_date 2025/10/14 · openalex updated_date 2026/07/28

Abstract

We study a family of fractional integral operators defined in ℝ³ whose kernels are distributions associated with Zygmund dilations: (x₁, x₂, x₃) → (δ₁ x₁, δ₂ x₂, δ₁δ₂ x₃) for δ₁,δ₂>0 having singularity on every coordinate subspace. As a result, we obtain a Hardy-Littlewood-Sobolev type inequality.

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