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Yuda_Dissertation.pdf (457.87 KB)
ETD Abstract Container
Abstract Header
Harmonic Bergman theory on punctured domains
Author Info
Wang, Yuda
Permalink:
http://rave.ohiolink.edu/etdc/view?acc_num=osu1650045277489607
Abstract Details
Year and Degree
2022, Doctor of Philosophy, Ohio State University, Mathematics.
Abstract
In the first part of this thesis, I develop a decomposition theorem for L^p harmonic functions on bounded domains in R ^n with smooth boundary that are punctured by removing a point. I apply this decomposition theorem to compute the harmonic Bergman kernel on the punctured smooth domains in terms of the harmonic Bergman kernel on the unpunctured smooth domains. Then I give a complete description of when basic duality and approximation properties hold for harmonic Bergman spaces and determine the L^p mapping properties of the harmonic Bergman projection. These findings reveal some unexpected dimension-dependent behavior of harmonic Bergman spaces that can occur for non-smooth domains. In the second part of this thesis, I develop a Laurent type series expansion for pluriharmonic functions on the generalized Hartogs triangle with a positive exponent. I apply this series expansion to compute the pluriharmonic Bergman kernel on these domains and explore the L^p boundedness of the associated pluriharmonic Bergman projection.
Committee
Kenneth Koenig (Advisor)
Pages
63 p.
Subject Headings
Mathematics
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Citations
Wang, Y. (2022).
Harmonic Bergman theory on punctured domains
[Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1650045277489607
APA Style (7th edition)
Wang, Yuda.
Harmonic Bergman theory on punctured domains.
2022. Ohio State University, Doctoral dissertation.
OhioLINK Electronic Theses and Dissertations Center
, http://rave.ohiolink.edu/etdc/view?acc_num=osu1650045277489607.
MLA Style (8th edition)
Wang, Yuda. "Harmonic Bergman theory on punctured domains." Doctoral dissertation, Ohio State University, 2022. http://rave.ohiolink.edu/etdc/view?acc_num=osu1650045277489607
Chicago Manual of Style (17th edition)
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Document number:
osu1650045277489607
Download Count:
191
Copyright Info
© 2022, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.