L^p-to-L^q boundedness for commutators of the Cauchy transform

2024/10/13 by Adam Mair, Mair, Adam
Mathematics · #42B20 #42B25 #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #FOS: Mathematics #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.2410.09966

openalex publication_date 2024/10/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we prove a characterization of the L^p-to-L^q boundedness of commutators to the Cauchy transform. Our work presents both new results and new proofs for established results. In particular, we show that the Campanato space characterizes boundedness of commutators for a certain range of p and q.

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