我們所要考慮的是乘積空間上的Calderon-Zygmund 算子，特別是在Hardy 空間上。在這乘積空間上，已知著名的結果只有Journe 的覆蓋引裡與Hardy 乘積空間上的原子分解。對於算子的有界性，則是在1987 年時Fefferman證明算子從H p (Rn × Rm )到 Lp (Rn × Rm )有界，直到2005 年時Han and Fan 才將結果推廣至H p有界。我所想要做的是減弱算子核的條件使他依舊滿足上述有界性，當然更進一步甚至考慮其加權空間有界性。 We will consider the Calderon-Zygmund operator on product spaces, especially product Hardy space. For the product domains, we only know Journe』s covering lemma and the atomic decomposition for the product Hardy spaces. For the boundedness of operators, 1987, Fefferman shows that they are bounded from H p (Rn × Rm ) to Lp (Rn × Rm ) . In 2005, Han and Fan extend to the H p -boundedness. Now, we are going to weaken the assumption of the kernel of operators to get the H p . Lp boundedness or H p -boundedness. Moreover, the weighted product spaces. 研究期間：9608 ~ 9707
