Harrison, Samuel Marcus (2010). Control of oscillatory convolution operators via maximal functions in weighted L\(^2\) inequalities. University of Birmingham. Ph.D.
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Harrison10PhD.pdf
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Abstract
This thesis is concerned with the weighted L\(^2\) boundedness of a family of convolution operators on the line with oscillating kernels. It is proved that these convolution operators are bounded from L\(^2\)(w) to L\(^2\)(W) where the Borel measures w and W are in a correspondence given by a maximal function and there is a sense in which this maximal function is the best possible. It is also shown that a one-weighted L\(^2\) estimate holds for a family of convolution operators with radial oscillating kernels on n-dimensional space.
| Type of Work: | Thesis (Doctorates > Ph.D.) | ||||||
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| Award Type: | Doctorates > Ph.D. | ||||||
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| College/Faculty: | Colleges (2008 onwards) > College of Engineering & Physical Sciences | ||||||
| School or Department: | School of Mathematics | ||||||
| Funders: | Engineering and Physical Sciences Research Council | ||||||
| Subjects: | Q Science > QA Mathematics | ||||||
| URI: | http://etheses.bham.ac.uk/id/eprint/1111 |
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