函数空间中关于积分算子的Wiener引理及有界性的研究

上世纪三十年代，N.Wiener给出了一个著名的结论：如果函数f处处不为零且具有绝对收敛的Fourier级数，那么1/f也具有绝对收敛的Fourier级数。这就是后来被人们称为经典的Wiener引理-稳定性。近年来，A.Aldroubi, A.Baskakov, I.Krishtal, R.Tessera, K.S.Kim, C.E.Shin和Q.Y. Sun等人研究了满足一定条件的算子的到自身的稳定性。最近，申请人, C. E. Shin 和Q.Y. Sun讨论了一类Bessel位势型奇异积分算子在上的稳定性。我们将研究更一般的情况，并且还考虑其它的函数空间。此外，在算子有界性方面，我们可以考虑极大函数N的交换子在带权Morrey 空间中的有界性及其等价刻画；还考虑参数Marcinkiewicz积分算子及其交换子和多线性分数次积分算子在带权Morrey 空间中的有界性。

The 1930s, N.Wiener gave a well-known conclusion: If the function f is not zero everywhere and has absolutely convergent Fourier series, 1/f also has absolutely convergent Fourier series. The above famous statement is now referred as the classical Wiener's Lemma- stability. In recent years, A.Aldroubi, A.Baskakov, I.Krishtal, R.Tessera, K.S Kim, C.E Shin and Q.Y Sun et al studied the operators who meet certain conditions is its own stability. Recently, the applicant, C.E Shin and Q.Y Sun considered a class of Bessel potential operators' stability. We will study more general case, and also consider other function spaces. In addition, on the boundedness of operators, we can consider the boundedness of maximal function N's commutators in weighted Morrey space and its equivalent characterizations; also consider the boundedness of parametric Marcinkiewicz integral operators and its commutators, and the multi-linear fractional integral operators in weighted Morrey spaces.