Multilinear estimates for maximal rough singular integrals

2024/08/31 by Bae Jun Park, Park, Bae Jun · 2 citations
Mathematics · #42B20 #42B25 #47H60 #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.2409.00357

openalex publication_date 2024/08/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this work, we establish L^p₁× ⋯× L^p_m→ L^p bounds for maximal multi-(sub)linear singular integrals associated with homogeneous kernels \fracΩ(\boldsymboly')|\boldsymboly|^mn where Ω is an L^q function on the unit sphere \mathbbS^mn-1 with vanishing moment condition and q>1. As an application, we obtain almost everywhere convergence results for the associated doubly truncated multilinear singular integrals.

Cited by

• Sharp bilinear estimates for maximal singular integrals with kernels in weighted L^q spaces
• An alternate approach to bilinear rough singular integrals

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