On pointwise a.e. convergence of multilinear operators

2020/12/20 by Loukas Grafakos, Grafakos, Loukas, Danqing He +5 · 3 citations
Mathematics · #42B15 #42B25 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Approximation Theory and Sequence Spaces #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2012.10837

openalex publication_date 2020/12/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this work we obtain the pointwise almost everywhere convergence for two families of multilinear operators: (a) truncated homogeneous singular integral operators associated with L^q functions on the sphere and (b) lacunary multiplier operators of limited decay. The a.e. convergence is deduced from the L²×⋯× L²→ L^2/m boundedness of the associated maximal multilinear operators.

Cited by

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

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