Multilinear proofs for convolution estimates for degenerate plane curves
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SCOPUS
- Title
- Multilinear proofs for convolution estimates for degenerate plane curves
- Authors
- Bak, JG
- Date Issued
- 2000-03
- Publisher
- CANADIAN MATHEMATICAL SOC
- Abstract
- Suppose that gamma is an element of C-2([0, infinity)) is a real-valued function such that gamma>(*) over bar * (0) = gamma'(0) = 0, and gamma double prime>(*) over bar * (t) approximate to t(m-2), for some integer m greater than or equal to 2. Let Gamma>(*) over bar * (t) = (t, gamma>(*) over bar * (t)), t > 0, be a curve in the plane, and let d lambda = dt be a measure on this curve. For a function f on R-2, let Tf(x) = (lambda *f))(x) = integral (infinity)(0) f(x - Gamma>(*) over bar * (t))dt, x is an element of R-2. An elementary proof is given for the optimal L-p-L-q mapping properties of T.
- Keywords
- HARMONIC-ANALYSIS
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/19827
- DOI
- 10.4153/CMB-2000-002-2
- ISSN
- 0008-4395
- Article Type
- Article
- Citation
- CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, vol. 43, no. 1, page. 17 - 20, 2000-03
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