{"id":{"repo_id":"rice","oai_identifier":"oai:repository.rice.edu:1911/89860"},"canonical_url":"https://search.dev.ndltd.org/etd/rice/oai:repository.rice.edu:1911/89860","repository":{"repo_id":"rice","name":"Rice University","base_url":"https://repository.rice.edu/server/oai/request"},"display":{"title":"Relations between two classes of singular integrals","abstract":"In 1952, Calderdn and Zygmund published a paper in which they discussed a certain kind of singular integral, and used some of their results to establish differential properties of solutions of Poisson's equation. Recently, Jones made some observations on the fundamental solution of the heat equation and gave another class of singular integrals. In this thesis it is shown that a special case of Jones's kernel is of Calderon-Zygmund type and a real, even kernel considered in [2] is a kernel of Jones's type if the coordinate system is suitably chosen. Moreover, for such kernels, the difference of the convolution operators-- defined in the sense of Jones and in the sense of CalderonZygmund, respectively--is a constant multiple of the identity operator.","abstract_html":"In 1952, Calderdn and Zygmund published a paper in which they discussed a certain kind of singular integral, and used some of their results to establish differential properties of solutions of Poisson's equation. Recently, Jones made some observations on the fundamental solution of the heat equation and gave another class of singular integrals. In this thesis it is shown that a special case of Jones's kernel is of Calderon-Zygmund type and a real, even kernel considered in [2] is a kernel of Jones's type if the coordinate system is suitably chosen. Moreover, for such kernels, the difference of the convolution operators-- defined in the sense of Jones and in the sense of CalderonZygmund, respectively--is a constant multiple of the identity operator.","abstract_has_math":false,"creators":["Tu, Chang-Char"],"institution":"Rice University","degree_name":"Master of Arts","degree_level":"Masters","degree_discipline":"Natural Sciences","degree_department":null,"school":null,"contributors":[],"advisors":["Jones, Frank"],"committee_chairs":[],"committee_members":[],"year":1964,"date_issued":"1964","date_published":"1964","updated_at":"2026-07-24T04:10:22Z","subjects":[],"languages":["eng"],"rights":["Copyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder."],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/1911/89860","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Jones, Frank"]},{"key":"dc:creator","label":"Author","values":["Tu, Chang-Char"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2016-04-22T21:58:47Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2016-04-22T21:58:47Z"]},{"key":"dc:date.issued","label":"Date","values":["1964"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Natural Sciences"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Masters"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Arts"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Rice University"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/1911/89860"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In 1952, Calderdn and Zygmund published a paper in which they discussed a certain kind of singular integral, and used some of their results to establish differential properties of solutions of Poisson's equation. Recently, Jones made some observations on the fundamental solution of the heat equation and gave another class of singular integrals. In this thesis it is shown that a special case of Jones's kernel is of Calderon-Zygmund type and a real, even kernel considered in [2] is a kernel of Jones's type if the coordinate system is suitably chosen. Moreover, for such kernels, the difference of the convolution operators-- defined in the sense of Jones and in the sense of CalderonZygmund, respectively--is a constant multiple of the identity operator."]},{"key":"dc:title","label":"Title","values":["Relations between two classes of singular integrals"]}]}],"canonical_facts":{"dc:contributor.advisor":["Jones, Frank"],"dc:creator":["Tu, Chang-Char"],"dc:date.accessioned":["2016-04-22T21:58:47Z"],"dc:date.available":["2016-04-22T21:58:47Z"],"dc:date.issued":["1964"],"dc:description.abstract":["In 1952, Calderdn and Zygmund published a paper in which they discussed a certain kind of singular integral, and used some of their results to establish differential properties of solutions of Poisson's equation. Recently, Jones made some observations on the fundamental solution of the heat equation and gave another class of singular integrals. In this thesis it is shown that a special case of Jones's kernel is of Calderon-Zygmund type and a real, even kernel considered in [2] is a kernel of Jones's type if the coordinate system is suitably chosen. Moreover, for such kernels, the difference of the convolution operators-- defined in the sense of Jones and in the sense of CalderonZygmund, respectively--is a constant multiple of the identity operator."],"dc:identifier.uri":["https://hdl.handle.net/1911/89860"],"dc:language.iso":["eng"],"dc:rights":["Copyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder."],"dc:title":["Relations between two classes of singular integrals"],"dc:type":["Thesis"],"thesis:degree_discipline":["Natural Sciences"],"thesis:degree_level":["Masters"],"thesis:degree_name":["Master of Arts"],"thesis:institution_name":["Rice University"]},"updated_at":"2026-07-24T04:10:22Z"}