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A class of singular integral operators with variable nuclear in some space bounded

Author: JiChunJing
Tutor: ZhaoKai
School: Qingdao University
Course: Basic mathematics
Keywords: Variable Kernels Singular integral operator Hardy space Herz type Hardy space Boundedness
CLC: O177
Type: Master's thesis
Year: 2007
Downloads: 43
Quote: 0
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Abstract


Harmonic analysis, Riesz transform has deep partial differential equations background, has been one of the people interested in issues surrounding its research, and achieved rich results. The fractional integral along all nuclear or rough nuclear is around the Riesz transform developed a very active topic. On the other hand, Calderon and Zygmund will be extended to the Riesz transform convolution operators - that is, the classical Calderon-Zygmund operator, which extended to the integral with variable nuclear operator. Although not in the true sense of the convolution operator integral operator with variable nuclear convolution ingredients, but also can be called, including \This article discusses the singular integral with variable nuclear operator and fractional integral operators. Along all nuclear fractional integral function space bounded many have been resolved, but with variable nuclear integral operator boundedness are still many imperfections. Recent years, with the improvement of function space decomposition theory, especially Herz type Hardy space molecular characterizations of perfection, so that we can further discuss with variable nuclear integral operator bounded. We utilize the existing results combined with the Hardy Space and Herz type Hardy space decomposition theory with variable nuclear singular integral operator and fractional integral operator new boundedness results on these two types of space. The main results are as follows: (i) for some 0 lt; p ≤ 1 satisfy the Dini condition given when the kernel function of the operator Ω (x, z) and with the variable nuclear singular integral operator vanishing moments conditions sub T Ω H p (R n ) to its own sector; (ii) under similar conditions with variable the nuclear fractional integral operator T Ω, μ to H q from the Hardy space H p (R n ) (R n ) (where q satisfy 1 / q = 1/p-μ/n) of Bounded Operators; (iii) When the kernel function Ω (x, z) satisfy certain conditions, with variable nuclear singular integral operator T Ω from the HK q α, p (R n ) the HK q α p (R n ) of a bounded operator; (iv) with variable nuclear integral operator T Ω, μ from HK q1 α, p1 (R n ) HK q2 α p2 (R n ) (q2 meet 1/q2 = 1/q1-μ/n) bounded.

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