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L^p and weighted L^2 estimates for barred derivatives in several complex variables.

Castillo, Andrew Z
http://rave.ohiolink.edu/etdc/view?acc_num=osu1605863773624004

Abstract Details

2020, Doctor of Philosophy, Ohio State University, 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.
Kenneth Koenig (Advisor)
Jeff McNeal (Committee Member)
Liz Vivas (Committee Member)
68 p.
Mathematics

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Citations

  • Castillo, A. Z. (2020). L^p and weighted L^2 estimates for barred derivatives in several complex variables. [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1605863773624004

    APA Style (7th edition)

  • Castillo, Andrew. L^p and weighted L^2 estimates for barred derivatives in several complex variables. . 2020. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1605863773624004.

    MLA Style (8th edition)

  • Castillo, Andrew. "L^p and weighted L^2 estimates for barred derivatives in several complex variables. ." Doctoral dissertation, Ohio State University, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=osu1605863773624004

    Chicago Manual of Style (17th edition)

osu1605863773624004
195
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