THE RESEARCH OF OPERATORS ON FUNCTION SPACES RELATED TO HARMONIC ANALYSIS

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Our purpose of this research is to study the properties of operators on function spaces related to harmonic analysis. Our investigators did the research at each special point. The content is as follows:Sato studied the properties of some bounded linear operators on Lorentz space associated with a measure space. In particular, by the application of the relation between Hankel transforms and Jacobi orthogonal system, he got the similar result with respect to the Lorentz multipliers of Jacobi orthogonal system to the result with respect to some bounded linear operators on the Lorentz space associated with Hankel transforms. Okayasu researched on essential definiteness, and semidefiniteness for tuples of operators, and Fejer's theorem on coefficients of positive trigonometric polynomials. Also he studied Korovkin type theorems on positive mappings of function spaces, essentially semidefinite operators, and positive trigonometric polynomials, and Korovkin type approximation. Mori has been d … More ealt with elimination theorems of defects of meroraorphic mappings of C"m into P"n(C). He showed an elimination theorem of defects of hypersurfaces in P"n(C) for a holomorphi curve of C into P"n(C), before. In this time, he proved an elimination theorem of defects of hypersurfaces in P"n(C) for a meroraorphic mapping of C"m into P"n(C). Mizuhara showed the weak factorization theorem of Lp-functions due to Morrey functions, blocks and the Riesz potential. Also applying this result, he showed the necessity for which the commutator between the Riesz potential and a locally integrable function to be bounded on Lp-spaces. Nakada studied the following: Let L be the limit set of a discontinuous group of Mobius transformations and let J be the Julia set of a rational function on the Riemann sphere. He studied the t-dimensional invariant probability measure on L and J to estimate the hausdorff dimension of these singular sets. Kawamura studied a generalization of chaotic maps to maps with n laps on a measure space and the behavior of the orbit of a probability density function. In this study he obtained some results concerning linear operators and Banach lattices. Sekigawa examined some exapraples of rational functions to study the connectivity of components of Fatou sets. He studied an inequality on the n-th derivatives of holomorphic functions of the open unit disk into itself. Less