MAXIMAL OPERATORS ASSOCIATED WITH SOME SINGULAR SUBMANIFOLDS
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Heo, Yaryong | - |
dc.contributor.author | Hong, Sunggeum | - |
dc.contributor.author | Yang, Chan Woo | - |
dc.date.accessioned | 2021-09-03T04:41:34Z | - |
dc.date.available | 2021-09-03T04:41:34Z | - |
dc.date.created | 2021-06-16 | - |
dc.date.issued | 2017-07 | - |
dc.identifier.issn | 0002-9947 | - |
dc.identifier.uri | https://scholar.korea.ac.kr/handle/2021.sw.korea/83040 | - |
dc.description.abstract | Let U be a bounded open subset of R-d and let Omega be a Lebesgue measurable subset of U. Let gamma = (gamma(1),...,gamma(n)) : U \ Omega -> R-n be a Lebesgue measurable function, and let mu be a Borel measure on Rd+n defined by <mu, f > = integral(d)(R)f(y,gamma(y))(sic)(y) xU\Omega(y) dy, where (sic) is a smooth function supported in U. In this paper we give some conditions under which the Fourier decay estimates vertical bar(mu) over cap(xi)vertical bar <= C(1+vertical bar xi vertical bar)(-epsilon) hold for some epsilon > 0. As a corollary we obtain the L-p- boundedness properties of the maximal operators M-S associated with a certain class of possibly non-smooth n-dimensional submanifolds of Rd+n, i.e., M(s)f(x) = sup r(-d) integral(vertical bar y vertical bar < r) vertical bar f(x-(y, gamma(y)))vertical bar x(R)d \Omega(sym) dy, r > 0 where Omega(sym) is a radially symmetric Lebesgue measurable subset of R-d,gamma(y) = (gamma(1)(y),...,gamma(n)(y)), gamma(i)(ty) = t(ai) gamma(i)(y) for each t > 0 where a(i) is an element of R, and the function gamma(i) : R-d\Omega(sym) -> R satisfies some singularity conditions over a certain subset of R-d. Also we investigate the endpoint (parabolic H-1, L-1,L-infinity) mapping properties of the maximal operators M-H associated with a certain class of possibly non-smooth hypersurfaces, i.e., M(H)f(x) = sup vertical bar integral(R)d f(x - (y, gamma(y)))r(-d)(sic)(r(-1)y)dy vertical bar , r > 0 where the function gamma : R-d -> R satisfies some singularity conditions over a certain subset of R-d and gamma(ty) = t(m) gamma(ty) for each t > 0 where m > 0. | - |
dc.language | English | - |
dc.language.iso | en | - |
dc.publisher | AMER MATHEMATICAL SOC | - |
dc.subject | PARABOLIC HP SPACES | - |
dc.subject | END-POINT ESTIMATE | - |
dc.subject | ATOMIC DECOMPOSITION | - |
dc.subject | ROUGH OPERATORS | - |
dc.title | MAXIMAL OPERATORS ASSOCIATED WITH SOME SINGULAR SUBMANIFOLDS | - |
dc.type | Article | - |
dc.contributor.affiliatedAuthor | Heo, Yaryong | - |
dc.contributor.affiliatedAuthor | Yang, Chan Woo | - |
dc.identifier.doi | 10.1090/tran/6785 | - |
dc.identifier.scopusid | 2-s2.0-85017301567 | - |
dc.identifier.wosid | 000399164000003 | - |
dc.identifier.bibliographicCitation | TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, v.369, no.7, pp.4597 - 4629 | - |
dc.relation.isPartOf | TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | - |
dc.citation.title | TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | - |
dc.citation.volume | 369 | - |
dc.citation.number | 7 | - |
dc.citation.startPage | 4597 | - |
dc.citation.endPage | 4629 | - |
dc.type.rims | ART | - |
dc.type.docType | Article | - |
dc.description.journalClass | 1 | - |
dc.description.journalRegisteredClass | scie | - |
dc.description.journalRegisteredClass | scopus | - |
dc.relation.journalResearchArea | Mathematics | - |
dc.relation.journalWebOfScienceCategory | Mathematics | - |
dc.subject.keywordPlus | PARABOLIC HP SPACES | - |
dc.subject.keywordPlus | END-POINT ESTIMATE | - |
dc.subject.keywordPlus | ATOMIC DECOMPOSITION | - |
dc.subject.keywordPlus | ROUGH OPERATORS | - |
dc.subject.keywordAuthor | Maximal operators | - |
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