奇异积分算子在加权调幅空间上的有界性

Mapping Properties of Singular Integral Operators on Weighted Modulation Spaces

调幅空间是调和分析中一类重要的函数空间,奇异积分算子是调和分析中的常见且重要的算子.为进一步研究此类算子在加权调幅空间上的有界性,文章主要利用函数分解和振荡积分估计证明某类沿曲线及曲面的奇异积分算子在加权调幅空间M_(s)^(p,q)(R^(2))上的有界性,其中0<p<1,0<q≤∞且s∈R.得到的主要结果对已有的有界性结论进行一定的补充,同时蕴含调幅空间比Lebesgue空间更适合研究奇异积分算子的映射性质.

Modulation spaces are an important function spaces in harmonic analysis,and singular integral op⁃erators are common and important operators in harmonic analysis.In order to further study the boundedness of such operators on weighted modulation spaces,the paper mainly uses function decomposition and oscillato⁃ry integral estimation to prove the mapping properties of certain singular integral operators along curves and surfaces on weighted modulation spaces M_(s)^(p,q)(R^(2)),where 0<p<1,0<q≤∞and s∈R.The main results of this article supplement the existing boundedness conclusions to some extent,and meanwhile imply that modu⁃lation spaces are more suitable for studying the mapping properties of singular integral operators than the Lebesgue spaces.