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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. Bennett, Jon Colleges (2008 onwards) > College of Engineering & Physical Sciences School of Mathematics QA Mathematics University of Birmingham 1111
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