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Jones, Frank Tu, Chang-Char 2016-04-22T21:58:47Z 2016-04-22T21:58:47Z 1964 Tu, 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/1911/89860 RICE0894 Thesis Math. 1964 Tu 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. 32 pp reformatted digital eng 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. Relations between two classes of singular integrals Thesis Text Mathematics Natural Sciences Rice University Masters Master of Arts open.access