2001 Fiscal Year Final Research Report Summary
Bergman classes and Hardy classes
| Project/Area Number |
10640156
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Shinshu University |
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Principal Investigator |
MATSUGU Yasuol Shinshu University, Faculty of Science, Professor, 理学部, 教授 (60020682)
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| Project Period (FY) |
1998 – 2000
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| Keywords | unit ball / Hardy space / Bergman space / Privalov space / Hardy-Orlicz space / Bergman-Orlicz space / invariant subspace / weighted Bergman-Orlicz space |
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| Research Abstract |
We studied on several function spaces of type of the Hardy spaces H^p( B_n ) and the Bergman spaces A^p( B_n ) ( 0<p<∞ ) on the unit ball B_n in the complex Euclidean space C^n. As important examples of the Hardy-Orlicz spaces H_φ( B_n ) and the weighted Bergman-Orlicz spaces A_φ( ν_α ) ( -1<α<∞ ) which contain the weighted Bergman spaces A^p(ν_α) ( -1<α<∞, 0<p<∞ ) generalizing the the Hardy spaces H^p( B_n ) and the Bergman spaces A^p(B_n ) ( 0<p<∞ ), the Privalov spaces N^p( B_n ) ( 1<p<∞ ) and the weighted Bergman- Privalov spaces ( AN )^p( ν_α ) ( -1<α<∞, 1 p<∞ ) have been studied in recent years. About these, we studied the invariant subspaces of the Privalov spaces N^p( B_1 ) ( 1<p<∞ ) and published the paper entitled "Invariant subspaces of the Privalov spaces"( Far East J.Math.Sci. vol.2 ). We also studied the linear isometries of the weighted Bergman-Privalov spaces ( AN )^p( ν_α ) ( -1<α<∞, 1 p<∞ ) and determined all of them ( to appear in J.Math.Soc. Japan ).This is a cooperative work with Ueki Sei-ichiro who is. a graduate student. Morover, we characterized the weighted Bergman-Orlicz spaces A_φ( ν_α ) ( -1<α<∞ ) in the same way as F.Beatrous-J.Burbea did the weighted Bergman spaces A_p( ν_α ) ( -1<α<∞, 0<p<∞ ) ( to appear in J.Austral. Math.Soc. ). We also characterized the weighted Bergman- Privalov spaces ( AN )^p( ν_α ) ( -1<α<∞, 1 p<∞ ) in the same way as S.Yamashita-M.Stoll-C.Ouyang-A. Zhao did the Hardy spaces H^p( B_n ) and the Bergman spaces A^p( B_n ) ( 0<p<∞ ). These are cooperative works with J.Miyazawa who is another graduate student. As the latest result, we have determined the continuous ring homomorphism of the the Privalov spaces N^p( B_n ) ( 1<p<∞ ) and the the weighted Bergman- Privalov spaces ( AN )^P( ν_α ) ( -1<α<∞, 1 p<∞ ). This is a cooperative work with Ueki Sei-ichiro, and we are preparing a paper on the result.
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Research Products
(11 results)
