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

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http://eprints.org/relation/isVolatileVersionOf http://etheses.bham.ac.uk/id/document/2769 http://eprints.org/relation/ispreviewThumbnailVersionOf http://etheses.bham.ac.uk/id/document/2769 http://eprints.org/relation/isVersionOf http://etheses.bham.ac.uk/id/document/2769 archive 4031 disk0/00/00/11/11 2010-11-22 12:40:50 2019-01-23 09:53:30 2011-07-19 16:29:30 thesis show 0 Harrison Samuel Marcus Bennett Jon University of Birmingham Control of oscillatory convolution operators via maximal functions in weighted L\(^2\) inequalities unpub QA 10col_ephy 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operators with radial oscillating kernels on n-dimensional space. 2010-12 2010-04 graduation eng author unchecked This unpublished thesis/dissertation is copyright of the author and/or third parties.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. public 127 University of Birmingham School of Mathematics d_ph FALSE epsrc 2010-12 graduation