2005 Fiscal Year Final Research Report Summary
Singular Integrals and Function Spaces
| Project/Area Number |
16540171
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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 | Tokai University |
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Principal Investigator |
KOMORI Yasuo Tokai University, School of High Technology for Human Welfare, Assistant Professor, 開発工学部, 助教授 (70234903)
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| Project Period (FY) |
2004 – 2005
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| Keywords | singular integral / Hardy space / nonhomogeneous space / 交換子作用素 |
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| Research Abstract |
We show that Calderon-Zygmund operator
Tf(x)=∫ K(x,y)f(y)dy
is bounded on some Lipschitz and Sobolev spaces if T1 belongs to Lipschitz space. As a corollary of our theorem, we show that Calderon's commutator
C_Af(x)=∫(A(x)-A(y))/(x-y)^2f(y)dy
is bounded on the spaces above.
We show that discrete singular integral operator
Tf(n)=Σ K(j)f(n-j)
is bounded on discrete Besov space B^{0,1}_1(Z) if the kernel K(n) satisfies some regularity conditions.
We define some maximal functions and weight classes on non-homogeneous spaces on R^n. And we show that these maximal functions are bounded on weighted L^p spaces.
We define Carleson measure with respect to non-doubling measure, and we show that Poisson integral operator is bounded from L^p(R^n) to L^p(R^{n+1}+), (upper half space).
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