Some Problems On The Operators Of Singular Integral

This PH. D thesis focuses on some problems about the boundedness and the convergence of integral operator. The paper consists of five chapters.In Chapter 1, we introduce some function spaces and some relevant operators.In Chapter 2, we consider the pointwise convergence of inverse of normal wavelet transform. Without the radial assumptions on the wavelet functions, we discuss the function is convergent at almost everywhere points. Our main theorem partly generalize and improve the results of Li and Sun [43], Weisz[64].In Chapter 3, we study characteristic of Parammetric Marcinkiewicz inte-grals on Hardy spaces. By atom decomposition, we obtain the boundedness of Parammetric Marcinkiewicz integrals ??? on weighted Hardy and weak weighted Hardy spaces which generalize the results in Hu and Wang[21], Ding, Lu and Xue[15], and improve the conditionIn Chapter 4, several questions on commutators of Hausdorff operators are considered. We consider the boundedness of generilized commutator of Hausdorff operators H?,?,A and then we discuss the multilinear commutator of Hausdorff operators H?,?,bf and prove its boundedness on Lebesgue spaces, Herz spaces and Morrey-Herz spaces. The definitions of H?,?,A,H?,?,b f may be found in Chapter 1.2.In Chapter 5, we discuss the multilinear operator with integral type kernel and get the weighted estimates of its commutator.