| Project/Area Number |
09640224
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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 |
解析学
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| Research Institution | Tokyo Woman's Christian University |
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Principal Investigator |
MIYACHI Akihiko Tokyo Woman's Christian University, College of Arts and Sciences ; Professor, 文理学部, 教授 (60107696)
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| Co-Investigator(Kenkyū-buntansha) |
NAGAYAMA Misao Tokyo Woman's Christian University, College of Arts and Sciences ; Lecturer, 文理学部, 講師 (30237557)
KOMURA Takako Tokyo Woman's Christian University, College of Arts and Sciences ; Professor, 文理学部, 教授 (60086345)
KONDO Takeshi Tokyo Woman's Christian University, College of Arts and Sciences ; Professor, 文理学部, 教授 (20012338)
TANIYAMA Kouki Tokyo Woman's Christian University, College of Arts and Sciences ; Associate Pro, 文理学部, 助教授 (10247207)
KOBAYASHI Kazuaki Tokyo Woman's Christian University, College of Arts and Sciences ; Professor, 文理学部, 教授 (50031323)
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| Project Period (FY) |
1997 – 1998
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| Project Status |
Completed (Fiscal Year 1998)
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| Budget Amount *help |
¥3,000,000 (Direct Cost: ¥3,000,000)
Fiscal Year 1998: ¥1,300,000 (Direct Cost: ¥1,300,000)
Fiscal Year 1997: ¥1,700,000 (Direct Cost: ¥1,700,000)
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| Keywords | Hardy space / Singular integral / Multilinear operator / Weighted Hardy space / Fractional integration / Sharp maximal function / Triebel-Lizorkin space / Hardy's theorem / ハ-ディ空間 / 特異積分作用素 / ソボレフ空間 / フーリエ変換 / ハ-ディの定理 |
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| Research Abstract |
1) We obtained H^p estimate for the multilinear operators which are finite sums of pointwise products of singular integrals. The class of singular integrals considered include the Calderon-Zygmund singular integrals and fractional integrations of arbitrary orders. We also obtained the estimates of those multilinear operators in other Hardy type spaces.
2) Using a sharp maximal function and the Lorentz spaces, we defined a function space which forms an algebra with respect to pointwise product of functions. This function space can be considered as a variant of the Sobolev space with the critical index.
3) Using purely real variable method, we showed that one can define the weighted Hardy spaces with respect to doubling measures on arbitrary open subset of R^n. This result extends those of Stromberg and Torchinsky which were given in the Springer Lecture Note #1381, 1989.
4) We proved two results conserning the extension of functions in A.Seeger's generalized Triebel-Lizorkin spaces.
5) We obtained a generalization of Hardy's clasical theorem on the Fourier transform.
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