Relations between two classes of singular integrals

[摘要] 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.

[发布机构] Rice University