- Bib ID:
- 3283638
- Format:
- Book and Microform
- Author:
- Tao, Terence Chi-Shen
- Description:
- 49 p.
- Summary:
-
In this dissertation we prove certain regularity properties of three unrelated families of operators arising from separate problems in harmonic analysis. The first result concerns the classical Bochner-Riesz operators $S\sp{\delta}$ on Euclidean spaces ${\rm\bf R}\sp{n}$ (as well as more general Riesz means on manifolds). By the work of C. Fefferman, P. Tomas, E. Stein, and M. Christ, one can obtain regularity results on these operators from $L\sp2$ restriction theory. We encompass these results by using the restriction theorem to prove an optimal weak-type estimate for the index $\delta={n-1\over2(n+1)},$ which is the sharpest possible result one can obtain from $L\sp2$ restriction theory alone.
The second result addresses the question of the pointwise convergence of various wavelet sampling methods. In applications one often samples a function
We show that a homogeneous singular integral convolution operator is of weak-type (1,1) if it is bounded on $L\sp2$ and the kernel is $L\log L$ on the sphere.
- Notes:
-
- (UnM)AAI9632989
- Source: Dissertation Abstracts International, Volume: 57-06, Section: B, page: 3784.
- Thesis (Ph.D.)--Princeton University, 1996.
- Reproduction:
- Microfiche. Ann Arbor, Mich.: University Microfilms International.
- Subject:
- Mathematics
- Other authors/contributors:
- Princeton University
- Copyright:
-
In Copyright
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Copyright status was determined using the following information:
- Material type:
- Literary Dramatic Musical
- Published status:
- Unpublished
- Creation date:
- 1996
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