Conjugate operator on variable harmonic Bergman space
| dc.contributor | Cruz-Uribe, David | |
| dc.contributor | Moen, Kabe | |
| dc.contributor | Shao, Yuanzhen | |
| dc.contributor | Gan, Yu | |
| dc.contributor.advisor | Ferguson, Timothy | |
| dc.contributor.author | Wang, Xuan | |
| dc.contributor.other | University of Alabama Tuscaloosa | |
| dc.date.accessioned | 2020-09-30T17:24:57Z | |
| dc.date.available | 2020-09-30T17:24:57Z | |
| dc.date.issued | 2020 | |
| dc.description | Electronic Thesis or Dissertation | en_US |
| dc.description.abstract | 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. | en_US |
| dc.format.extent | 35 p. | |
| dc.format.medium | electronic | |
| dc.format.mimetype | application/pdf | |
| dc.identifier.other | u0015_0000001_0003624 | |
| dc.identifier.other | Wang_alatus_0004D_14133 | |
| dc.identifier.uri | http://ir.ua.edu/handle/123456789/7023 | |
| dc.language | English | |
| dc.language.iso | en_US | |
| dc.publisher | University of Alabama Libraries | |
| dc.relation.hasversion | born digital | |
| dc.relation.ispartof | The University of Alabama Electronic Theses and Dissertations | |
| dc.relation.ispartof | The University of Alabama Libraries Digital Collections | |
| dc.rights | All rights reserved by the author unless otherwise indicated. | en_US |
| dc.subject | Mathematics | |
| dc.title | Conjugate operator on variable harmonic Bergman space | en_US |
| dc.type | thesis | |
| dc.type | text | |
| etdms.degree.department | University of Alabama. Department of Mathematics | |
| etdms.degree.discipline | Mathematics | |
| etdms.degree.grantor | The University of Alabama | |
| etdms.degree.level | doctoral | |
| etdms.degree.name | Ph.D. |
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