1998 Fiscal Year Final Research Report Summary
Research on singular integral operators and function spaces
| Project/Area Number |
09640224
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
解析学
|
|---|
| Research Institution | Tokyo Woman's Christian University |
|---|
Principal Investigator |
MIYACHI Akihiko Tokyo Woman's Christian University, College of Arts and Sciences ; Professor, 文理学部, 教授 (60107696)
|
|---|
| 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)
|
|---|
| Project Period (FY) |
1997 – 1998
|
| Keywords | Hardy space / Singular integral / Multilinear operator / Weighted Hardy space / Fractional integration / Sharp maximal function / Triebel-Lizorkin space / Hardy's theorem |
|---|
| 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.
|
Research Products
(11 results)
