Results, Several Bounded On The Hardy-lorentz Spaces

In this thesis, some basic knowledge of weighted weak H1 spaces are intro-duced. By the atomic decomposition of weighted weak H1 spaces, we obtain the weighted boundedness of Marcinkiewicz integral operators on weak H1 spaces. Then, the definitions and atomic decompositions of Hardy-Lorentz spaces are introduced, which are the intermediate spaces between Hardy spaces. Moti-vated by the theory of weak Hardy spaces and the boundedness of operators on weak Hardy spaces, Hardy-Lorentz spaces are discussed. By the atomic decom-position of Hardy-Lorentz spaces, using the results of boundedness of operators on Lp, and the inequality estimates, we discuss the boundedness of some classic operators and commutators. Thus, the boundedness of Marcinkiewicz integral operators from certain Hardy-Lorentz spaces to Lp,∞(Rn) spaces is obtained. Beside, the commutators generated by BMO founctions b and Littlewood-Paley operators and Calderon-Zygmund operators are bounded from certain Hardy-Lorentz spaces to Lp,∞(Rn) spaces.