Boundedness And Convergence Of Some Wavelet Operators

The thesis consists of five chapters.The first Chapter is an introduction.In Chapter 2, we determine the jumps of functions by using conjugate oper-tors. Moreover, we solve the open problem publishing on " Science in China " which was proposed by X. L. Shi and L. Hu in 2008.In Chapter 3, we improve and generalize a result was proved by A. Zayed in Proc. Amer. Math. Soc..In Chapter 4, we discuss the boundedness of frame operators and improve criteria for unconditional wavelet bases in Lp(Rn) established by C. K. Chui-X L. Shi and I. Daubechies.In Chapter 5, through the study of Bessel control functions, we establish a new criterion for Bessel sequences by Bessel control functions.