Fractional integral on Hardy spaces on product domains

2025/09/03 by Yiyu Tang, Tang, Yiyu
Mathematics · #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2509.03158

openalex publication_date 2025/09/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

By using the vector-valued theory of singular integrals, we prove a Hardy--Littlewood--Sobolev inequality on product Hardy spaces H^p_\rmprod, which is a parallel result of the classical Hardy--Littlewood--Sobolev inequality. The same technique shows the H^p_\rmprod-boundedness of the iterated Hilbert transform. As a byproduct, new proofs of several recently discovered Hardy type inequalities on product Hardy spaces are obtained, which avoid complicated Calderón--Zygmund theory on product domain, rendering them considerably simpler than the original proofs.

Citations

• Hardy-Littlewood-type theorems for Fourier transforms in \R^d

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