Conjugate operator on variable harmonic Bergman space

Complex analytic functions have astonishing and amazing properties. Their real parts and imaginary parts are deeply connected by the Cauchy-Riemann equations. It is natural to ask if we obtain some information about the real part, what can we conclude about the imaginary part, which is called the harmonic conjugate of the real part? Treating the relationship as an operation, the question becomes how well behaved is the harmonic conjugate operator? In this paper, by modifying some classical methods in constant exponent Hardy and Bergman spaces and developing new ways for the modern variable exponent spaces, we will study the harmonic conjugate operator on variable exponent Bergman spaces and prove that the operator is bounded when the exponent has positive minimum and finite maximum and satisfies the log-Holder condition.

Grantor dc:publisher

University of Alabama Libraries

Year dc:date.issued

2020

Author dc:creator

• Wang, Xuan

Advisor dc:contributor.advisor

• Ferguson, Timothy

Contributors dc:contributor

• Cruz-Uribe, David
• Moen, Kabe
• Shao, Yuanzhen
• Gan, Yu

• Mathematics

Statement dc:rights

• All rights reserved by the author unless otherwise indicated.

Language dc:language.iso

en_US, English

Dc Identifier Other

u0015_0000001_0003624
Wang_alatus_0004D_14133

OAI identifier oai:identifier

oai:ir.ua.edu:123456789/7023