THE RESEARCH OF WEAK TYPE OPERATORS ON FUNCTION SPACES

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Sato studied the properties of Fourier multipliers on locally Compact abelian groups. In particular, he got some results with respect to Lp-improving multipliers and Lorentz-improving multipliers, and published the results. Okayasu studied that the Lowner-Heinz inequality was shown for strictly positive elements of unital hermitian Banacb*-algebras, via the Cordes inequality which was also shown for same objects. Also be studied that several results were gotten on linear isometries on function spaces, and on operator spaces. Mon got an elimination theorem of Nevanlinna defects of holomorphic curves into Pn(C) for rational moving targets. Also, he considered to introduce a distance in the space of holomorpbic(or meromorphic) mappings into Pn(C), and obtained a distance in this space. Then holomorphic (or mieromorphic) mappings into Pn(C) without Nevanlinna defects are densein this space. Itizuhara showed the boundedness of commutators (b, T], between some singular integral operator and … More multiplication operator by a locally integrable function bon Morrey spaces Lpg(Rn) with general growth function g, This results generalize partly the classical results due to Di Fazio and Ragusa. Also he obtained some new results. Nakada studied the following subject by the method of complex analysis. Firstly, the region of discontinuities and the limit sets of discontinuous groups acting on the Riemann sphere. Secondary, the Fatou sets and Julia sets arise from complex dynamics of rational maps of the Riemarin sphere. Kawamura studied some chaotic properties in topological dynamical systems by using the theory of operator algebras. Considering topological dynamical systems in the sense of probability theory, he tried to analyze them on the Hubert space and obtained some relations between our study of topological dynamics and wavelet theory. Sekigawa investigated the Ford fundamental regions for the cyclic groups generated by some parabolic Mobius transformations acting on the 3-dimensional Euclidean space, by using the Clifford matrix representation of liobius transformations. Harada studied algebraic theory of coding theory over finite rings, and codes over finite rings with relationships to other topics. Less