Dissertation
The Generalization of Fatou’s Theorem and Its Converse
Washington State University
Doctor of Philosophy (PhD), Washington State University
2023
DOI:
https://doi.org/10.7273/000005380
Abstract
We consider a function K(x) on R n which satisfies certain decay conditions. Let µ be a signed measure on R n . For y > 0 set K[µ](x, y) = Z Rn 1 y n K( x − t y )dµ(t). In this paper we investigate the relationship between the derivative of µ at a point x ∈ R n and the non-tangential limit of K[µ](x, y) (thought of as a function in R n+1 + ).
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Details
- Title
- The Generalization of Fatou’s Theorem and Its Converse
- Creators
- Tariq Alsmadi
- Contributors
- Charles Moore (Advisor)Alexander Panchenko (Committee Member)Alex Khapalov (Committee Member)
- Awarding Institution
- Washington State University
- Academic Unit
- Mathematics and Statistics, Department of
- Theses and Dissertations
- Doctor of Philosophy (PhD), Washington State University
- Publisher
- Washington State University
- Number of pages
- 84
- Identifiers
- 99901031139201842
- Language
- English
- Resource Type
- Dissertation