In this thesis we study three topics in Harmonic Analysis in the finite field setting. The methods used are purely combinatorial in nature. We prove a sharp result for the maximal operator associated to dilations of quadric surfaces. We use Christ’s method ([Christ, Convolution, Curvature and Combinatorics. A case study, International Math. Research Notices 19 (1998)]), for L<sup>p</sup>→ L<sup>q</sup> estimates for convolution with the twisted n-bic curve in the European setting, to give L<sup>p</sup> → L<sup>q</sup> estimates for convolution with k-dimensional surfaces in the finite field setting. We give solution to the k-plane Radon transform problem and embark on a study of a generalisation of this problem.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:662516 |
| Date | January 2005 |
| Creators | Stones, Brendan |
| Publisher | University of Edinburgh |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://hdl.handle.net/1842/14492 |
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