Dissertation
Fractional Integral Operators
Washington State University
Doctor of Philosophy (PhD), Washington State University
01/2021
DOI:
https://doi.org/10.7273/000003146
Handle:
https://hdl.handle.net/2376/122972
Abstract
This work serves as an extension of classical harmonic analysis and Calderón-Zygmund theory.
In particular, in this work concerns the control of generalized integral operators in terms
of certain maximal functions. The primary setting of this work is a non homogeneous metric
space with a measure that is not necessarily doubling.
We characterize fractional kernel functions on a space (X; d), a metric measure space
equipped with a positive Radon measure . It is shown that the integral operators associated
with these kernels reveal properties of certain convolution operators in terms of
certain maximal operators. A Hedberg-type inequality is established, connecting our results
to the Hardy-Littlewood-Weiner maximal theorem. A generalized good- inequality is established,
connecting the distribution function of a fractional potential to its corresponding
fractional maximal function. Other potential estimates are established, revealing properties
of the Riesz potentials.
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Details
- Title
- Fractional Integral Operators
- Creators
- Adebowale Sijuwade
- Contributors
- Charles N. Moore (Advisor)Alexander Khapalov (Committee Member)Xueying Wang (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
- 96
- Identifiers
- 99900651901401842
- Language
- English
- Resource Type
- Dissertation