Holomorphic extension on product Lipschitz surfaces in two complex\n variables

2014/01/10 by Jarod Hart, Alessandro Monguzzi, Hart, Jarod +1
Mathematics · #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1401.2361

openalex publication_date 2014/01/10 · openalex created_date 2022/09/13 · openalex updated_date 2026/07/28

Abstract

In this work we prove a new L^p holomorphic extension result for functions\ndefined on product Lipschitz surfaces with small Lipschitz constants in two\ncomplex variables. We define biparameter and partial Cauchy integral operators\nthat play the role of boundary values for holomorphic functions on product\nLipschitz domain. In the spirit of the application of David-Journ 'e-Semmes and\nChrist's Tb theorem to the Cauchy integral operator, we prove a biparameter\nTb theorem and apply it to prove L^p space bounds for the biparameter\nCauchy integral operator. We also prove some new biparameter\nLittlewood-Paley-Stein estimates and use them to prove the biparameter Tb\ntheorem.\n

Citations

• A T(1) theorem on product spaces
• A Bilinear T(b) Theorem for Singular Integrals
• Multilinear Calderón–Zygmund Theory
• Hp spaces of several variables

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