DC Field | Value | Language |
---|---|---|
dc.contributor.author | Kuk, Seung-Woo | ko |
dc.contributor.author | Lee, Sung-Yun | ko |
dc.date.accessioned | 2013-06-07T09:13:55Z | - |
dc.date.available | 2013-06-07T09:13:55Z | - |
dc.date.created | 2013-05-24 | - |
dc.date.created | 2013-05-24 | - |
dc.date.issued | 2012 | - |
dc.identifier.citation | MATHEMATICAL RESEARCH LETTERS, v.19, no.5, pp.1145 - 1154 | - |
dc.identifier.issn | 1073-2780 | - |
dc.identifier.uri | http://hdl.handle.net/10203/173944 | - |
dc.description.abstract | We prove that the multilinear fractional integral operator I-alpha(f(1), ... , f(k))(x) = integral(Rn) f(1)(x-theta(1y)) ... f(k)(x-theta(ky))vertical bar y vertical bar(alpha-n)dy, where theta(j), j = 1, ... , k are distinct and nonzero, (due to Grafakos [G]) has the endpoint weak-type boundedness into L-r,L-infinity when r = n/2n-alpha. Hence, we obtain by the multilinear interpolation theorem that I-alpha is bounded into L-r for all r > n/2n-alpha. Moreover, We also prove that I-alpha is not bounded into L-r for any r < n/2n-alpha under some conditions on theta(j)'s. Similarly, we show that the multilinear Hilbert transform H(f, g, h(1) ,... , h(k))(x) = p.v. integral f(x + t) g(x - t) Pi(k)(j=1) h(j) (x - theta(j)t)dt/t, where theta(j) not equal +/- 1 are distinct and nonzero, is not bounded into L-r for any r < 1/2 under some conditions on theta(j)'s. | - |
dc.language | English | - |
dc.publisher | INT PRESS BOSTON, INC | - |
dc.subject | INTERPOLATION | - |
dc.title | ENDPOINT BOUNDS FOR MULTILINEAR FRACTIONAL INTEGRALS | - |
dc.type | Article | - |
dc.identifier.wosid | 000317587200015 | - |
dc.identifier.scopusid | 2-s2.0-84876894400 | - |
dc.type.rims | ART | - |
dc.citation.volume | 19 | - |
dc.citation.issue | 5 | - |
dc.citation.beginningpage | 1145 | - |
dc.citation.endingpage | 1154 | - |
dc.citation.publicationname | MATHEMATICAL RESEARCH LETTERS | - |
dc.contributor.localauthor | Lee, Sung-Yun | - |
dc.type.journalArticle | Article | - |
dc.subject.keywordPlus | INTERPOLATION | - |
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