# Control of oscillatory convolution operators via maximal functions in weighted L$$^2$$ inequalities

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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## 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.)
Award Type: Doctorates > Ph.D.
Supervisor(s):
Supervisor(s)EmailORCID
Bennett, JonUNSPECIFIEDUNSPECIFIED
Licence:
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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