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Boundary behavior of the Bergman kernel function on strongly pseudoconvex domains with respect to weighted Lebesgue measure

Kennell, Lauren R.

Abstract Details

2005, Doctor of Philosophy, Ohio State University, Mathematics.
The author proves pointwise estimates for the weighted Bergman kernel and its derivatives near the boundary of a smoothly bounded, strongly pseudoconvex domain. The estimate is obtained by relating the Bergman kernel to the Neumann operator, and estimating the Neumann operator using certain biholomorphic coordinate changes chosen to take advantage of the boundary geometry. The result obtained says, essentially, that a weight function which is smooth up to the boundary of the domain neither improves nor worsens the singularity of the kernel near the boundary diagonal.
Jeffery McNeal (Advisor)
86 p.

Recommended Citations

Citations

  • Kennell, L. R. (2005). Boundary behavior of the Bergman kernel function on strongly pseudoconvex domains with respect to weighted Lebesgue measure [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1121801617

    APA Style (7th edition)

  • Kennell, Lauren. Boundary behavior of the Bergman kernel function on strongly pseudoconvex domains with respect to weighted Lebesgue measure. 2005. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1121801617.

    MLA Style (8th edition)

  • Kennell, Lauren. "Boundary behavior of the Bergman kernel function on strongly pseudoconvex domains with respect to weighted Lebesgue measure." Doctoral dissertation, Ohio State University, 2005. http://rave.ohiolink.edu/etdc/view?acc_num=osu1121801617

    Chicago Manual of Style (17th edition)