{"id":{"repo_id":"birmingham","oai_identifier":"oai:etheses.bham.ac.uk:1111"},"canonical_url":"https://search.dev.ndltd.org/etd/birmingham/oai:etheses.bham.ac.uk:1111","repository":{"repo_id":"birmingham","name":"University of Birmingham","base_url":"https://etheses.bham.ac.uk/cgi/oai2"},"display":{"title":"Control of oscillatory convolution operators via maximal functions in weighted L\\(^2\\) inequalities","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.","abstract_html":"This thesis is concerned with the weighted L<span class=\"etd-inline-math\"><sup>2</sup></span> boundedness of a family of convolution operators on the line with oscillating kernels. It is proved that these convolution operators are bounded from L<span class=\"etd-inline-math\"><sup>2</sup></span>(w) to L<span class=\"etd-inline-math\"><sup>2</sup></span>(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<span class=\"etd-inline-math\"><sup>2</sup></span> estimate holds for a family of convolution operators with radial oscillating kernels on n-dimensional space.","abstract_has_math":true,"creators":["Harrison, Samuel Marcus"],"institution":"University of Birmingham","degree_name":"d_ph","degree_level":"d_ph","degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2010,"date_issued":"2010-12","date_published":"2010-12","updated_at":"2026-07-24T01:11:23Z","subjects":["QA Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":null,"outbound_label":null,"outbound_source":null},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.sponsor","label":"Sponsor","values":["epsrc"]},{"key":"dc:creator","label":"Author","values":["Harrison, Samuel Marcus"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2010-12"]},{"key":"dc:date.issued","label":"Date","values":["2010-12"]},{"key":"dc:publisher.department","label":"Dc Publisher Department","values":["College of Engineering & Physical Sciences","School of Mathematics"]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["University of Birmingham"]},{"key":"dc:relation.isreferencedby","label":"Dc Relation Isreferencedby","values":["http://etheses.bham.ac.uk//id/eprint/1111/"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["d_ph"]},{"key":"dc:type.qualificationname","label":"Dc Type Qualificationname","values":["d_ph"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["QA Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://etheses.bham.ac.uk//id/eprint/1111/1/Harrison10PhD.pdf","http://etheses.bham.ac.uk//id/eprint/1111/2/Decl_IS_Harrison10PhD.pdf"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Control of oscillatory convolution operators via maximal functions in weighted L\\(^2\\) inequalities"]}]}],"canonical_facts":{"dc:contributor.sponsor":["epsrc"],"dc:creator":["Harrison, Samuel Marcus"],"dc:date":["2010-12"],"dc:date.issued":["2010-12"],"dc:description.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."],"dc:format":["application/pdf"],"dc:identifier.uri":["http://etheses.bham.ac.uk//id/eprint/1111/1/Harrison10PhD.pdf","http://etheses.bham.ac.uk//id/eprint/1111/2/Decl_IS_Harrison10PhD.pdf"],"dc:publisher.department":["College of Engineering & Physical Sciences","School of Mathematics"],"dc:publisher.institution":["University of Birmingham"],"dc:relation.isreferencedby":["http://etheses.bham.ac.uk//id/eprint/1111/"],"dc:subject":["QA Mathematics"],"dc:title":["Control of oscillatory convolution operators via maximal functions in weighted L\\(^2\\) inequalities"],"dc:type":["Thesis"],"dc:type.qualificationlevel":["d_ph"],"dc:type.qualificationname":["d_ph"]},"updated_at":"2026-07-24T01:11:23Z"}