Taiwanese Journal of Mathematics

INTEGRAL PRODUCTS, BOCHNER-MARTINELLI TRANSFORMS AND APPLICATIONS

Chia-Chi Tung

Full-text: Open access

Abstract

A generalized Bochner-Martinelli formula for the push-forward of a Lipschitz function over a weak Stokes domain is proved. By means of integral products, the $\bar \partial$-Euler and the $\bar \partial$-Neumann vector fields, local and global characterizations of the holomorphicity of functions on a Riemann domain are given. As further applications characterizations of isogeneity and Liouville properties for the push-forward of semi-harmonic functions on an analytic covering space are obtained.

Article information

Source
Taiwanese J. Math., Volume 13, Number 5 (2009), 1583-1608.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500405559

Digital Object Identifier
doi:10.11650/twjm/1500405559

Mathematical Reviews number (MathSciNet)
MR2554476

Zentralblatt MATH identifier
1181.31004

Subjects
Primary: 31C05: Harmonic, subharmonic, superharmonic functions
Secondary: 32C30: Integration on analytic sets and spaces, currents {For local theory, see 32A25 or 32A27} 31B10: Integral representations, integral operators, integral equations methods

Keywords
semi-Riemann domain $\bar \partial$-Euler vector field $\bar \partial$-Neumann vector field semi-harmonicity Dirichlet product push-forward Bochner-Martinelli transform

Citation

Tung, Chia-Chi. INTEGRAL PRODUCTS, BOCHNER-MARTINELLI TRANSFORMS AND APPLICATIONS. Taiwanese J. Math. 13 (2009), no. 5, 1583--1608. doi:10.11650/twjm/1500405559. https://projecteuclid.org/euclid.twjm/1500405559


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