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Control of oscillatory convolution operators via maximal functions in weighted L\(^2\) inequalities

Harrison, Samuel Marcus (2010)
Ph.D. thesis, University of Birmingham.

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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:Ph.D. thesis.
Supervisor(s):Bennett, Jon
School/Faculty:Colleges (2008 onwards) > College of Engineering & Physical Sciences
Department:School of Mathematics
Subjects:QA Mathematics
Institution:University of Birmingham
ID Code:1111
This unpublished thesis/dissertation is copyright of the author and/or third parties. The intellectual property rights of the author or third parties in respect of this work are as defined by The Copyright Designs and Patents Act 1988 or as modified by any successor legislation. Any use made of information contained in this thesis/dissertation must be in accordance with that legislation and must be properly acknowledged. Further distribution or reproduction in any format is prohibited without the permission of the copyright holder.
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