L^p and weighted L^2 estimates for barred derivatives in several complex variables.
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The Ohio State University / OhioLINK
2020
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| Online Access: | http://rave.ohiolink.edu/etdc/view?acc_num=osu1605863773624004 |
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ndltd-OhioLink-oai-etd.ohiolink.edu-osu16058637736240042021-10-02T05:10:33Z L^p and weighted L^2 estimates for barred derivatives in several complex variables. Castillo, Andrew Z. Mathematics We generalize the basic L^2 inequalities for barred derivatives on smooth bounded pseudoconvex domains. Using techniques from harmonic analysis and mapping properties of the dbar-Neumann operator, we prove that on smooth bounded pseudoconvex domains of finite type with comparable Levi eigenvalues that for every s ge 0 and 1pinfty, there exists a positive constant C_p,s such that a L^p estimate holds. Furthermore, similar L^p Sobolev estimates hold on all smooth bounded weakly q-convex domains but with a loss of derivatives. In the second part of this thesis, we prove various weighted L^2 estimates where the weight in question is comparable to a power of the distance to the boundary. In particular, utilizing an energy identity and a local decomposition of forms, we prove a weighted L^2 estimate on smooth bounded weakly q-convex domains when -1/2s1/2. We conclude by showing that even when a subelliptic estimate holds, there can be no gain in the weighted L^2 norms for barred derivatives. 2020 English text The Ohio State University / OhioLINK http://rave.ohiolink.edu/etdc/view?acc_num=osu1605863773624004 http://rave.ohiolink.edu/etdc/view?acc_num=osu1605863773624004 unrestricted This thesis or dissertation is protected by copyright: all rights reserved. It may not be copied or redistributed beyond the terms of applicable copyright laws. |
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NDLTD |
| language |
English |
| sources |
NDLTD |
| topic |
Mathematics |
| spellingShingle |
Mathematics Castillo, Andrew Z. L^p and weighted L^2 estimates for barred derivatives in several complex variables. |
| author |
Castillo, Andrew Z. |
| author_facet |
Castillo, Andrew Z. |
| author_sort |
Castillo, Andrew Z. |
| title |
L^p and weighted L^2 estimates for barred derivatives in several complex variables. |
| title_short |
L^p and weighted L^2 estimates for barred derivatives in several complex variables. |
| title_full |
L^p and weighted L^2 estimates for barred derivatives in several complex variables. |
| title_fullStr |
L^p and weighted L^2 estimates for barred derivatives in several complex variables. |
| title_full_unstemmed |
L^p and weighted L^2 estimates for barred derivatives in several complex variables. |
| title_sort |
l^p and weighted l^2 estimates for barred derivatives in several complex variables. |
| publisher |
The Ohio State University / OhioLINK |
| publishDate |
2020 |
| url |
http://rave.ohiolink.edu/etdc/view?acc_num=osu1605863773624004 |
| work_keys_str_mv |
AT castilloandrewz lpandweightedl2estimatesforbarredderivativesinseveralcomplexvariables |
| _version_ |
1719486449495048192 |