THE RESEARCH OF OPERATORS ON LORENTZ SPACES BY THE METHOD OF HARMONIC ANALYSIS

点击翻译按钮获取中文摘要

Our purpose of this research is to study the properties of operators on Lorentz spaces by the method of haomonic analysis. Our investigations did the research at each special point. The content is as follows :Sato studied the relation between some operators of Hankel transforms and the operators of Jacobi orthgonal system on (0,pi). Also he studied an inequality related to the operators on the Lorentz-Zygmund spaces. Mori researched about a problem of constructions of algebraically nondegenereate meromorophic mappings and the uniquness problem related to meromorphic functions. Mizuhara showed the weak factorization theorem of H^1-functions due to generalized Morrey functions, blocks and the Riesz potential. Also applying this result, he observed the necessity for which the commutator between the Reisz potential and a locally integrable function to be bounded on the generalized Morrey spaces. Nakada studied some geometric properties of the Julia set of rational functions on the Riemann sphere. Kawamura discussed an generalization of the theory concerning the behavior of probability density functions associated with chaotic maps on a measure space. He studied conjugacy of new type connecting two chaotic maps. Sekigawa studied the M"obious transformations on the high dimensional Euclidean spaces, by using Clifford matrix representations of M"obious transformations. Kanjin showed the boundedness of the transplantation operators concerning the Hankel transform on the Hardy spaces. Also he showed the boundedness of Cesaro operators, and Hardy's inequality related to the Fourier coefficients with respect to the Jacobi series on the Hardy's space.