奇异卷积算子在加权Wiener共合空间上的有界性

Boundedness Properties of the Singular Convolution Operators on Weighted Wiener Amalgam Space

奇异积分算子是调和分析中常见的一类算子,大量数学工作者都在研究其在各类函数空间上的有界性。众所周知,奇异卷积算子是一种特殊的奇异积分算子,研究其相关性质是值得讨论的,主要利用振荡积分估计证明了奇异卷积算子在加权Wiener共合空间W(FLs^p,Lq)上的有界性,从最终的结论可以看出指标p的范围比Lebesgue空间上的要大很多,这说明Wiener共合空间的性质比Lebesgue空间要好。

Singular integral operator is a kind of common operator in harmonic analysis. Many mathematicians are studying its boundedness in various function spaces. Singular convolution operator is a kind of special singular integral operator, and its related properties are worth studying. In this paper the oscillatory integral estimation is used to prove the boundedness properties of the singular convolution operator on weighted Wiener amalgam space W(FLs^p,Lq). We can see from the final conclusion that the range of index p is much larger than that in Lebesgue space, which means that the properties of the Wiener amalgam space are better than that of the Lebesgue space.