Jones, Frank2016-04-222016-04-221964Tu, Chang-Char. "Relations between two classes of singular integrals." (1964) Master’s Thesis, Rice University. <a href="https://hdl.handle.net/1911/89860">https://hdl.handle.net/1911/89860</a>.https://hdl.handle.net/1911/89860In 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.32 ppengCopyright 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.ThesisRICE0894reformatted digitalThesis Math. 1964 Tu