A Maximal Function Associated to the Curve (t, t2)
The authors prove that Mf(x, y) = $\underset h>0\to{\sup}$ (1/h) ∫-hh|(f(x - t, y - t2)|dt is bounded from Lp(R2) to Lp(R2) for 1 < p ≤ ∞ .
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Published in | Proceedings of the National Academy of Sciences - PNAS Vol. 73; no. 5; pp. 1416 - 1417 |
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Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
United States
National Academy of Sciences of the United States of America
01.05.1976
National Acad Sciences |
Subjects | |
Online Access | Get full text |
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Abstract | The authors prove that Mf(x, y) = $\underset h>0\to{\sup}$ (1/h) ∫-hh|(f(x - t, y - t2)|dt is bounded from Lp(R2) to Lp(R2) for 1 < p ≤ ∞ . |
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AbstractList | THE AUTHORS PROVE THAT [FORMULA: see text] is bounded from L(P)(R(2)) to L(P)(R(2)) for 1 < p </= infinity. THE AUTHORS PROVE THAT [FORMULA: see text] is bounded from L(P)(R(2)) to L(P)(R(2)) for 1 < p </= infinity. The authors prove that [Formula: see text] is bounded from L P ( R 2 ) to L P ( R 2 ) for 1 < p ≤ ∞. The authors prove that [Formula: see text] is bounded from L P ( R 2 ) to L P ( R 2 ) for 1 < p ≤ ∞. Euclidean harmonic analysis norm estimates The authors prove that Mf(x, y) = $\underset h>0\to{\sup}$ (1/h) ∫-hh|(f(x - t, y - t2)|dt is bounded from Lp(R2) to Lp(R2) for 1 < p ≤ ∞ . |
Author | Nagel, Alexander Wainger, Stephen Riviere, Nestor |
AuthorAffiliation | University of Wisconsin, Madison, Wisc. 53706 Institute for Advanced Study, Princeton, New Jersey 08540 University of Minnesota, Minneapolis, Minn. 55455 |
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Author_xml | – sequence: 1 givenname: Alexander surname: Nagel fullname: Nagel, Alexander – sequence: 2 givenname: Nestor surname: Riviere fullname: Riviere, Nestor – sequence: 3 givenname: Stephen surname: Wainger fullname: Wainger, Stephen |
BackLink | https://www.ncbi.nlm.nih.gov/pubmed/16592317$$D View this record in MEDLINE/PubMed |
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Snippet | The authors prove that Mf(x, y) = $\underset h>0\to{\sup}$ (1/h) ∫-hh|(f(x - t, y - t2)|dt is bounded from Lp(R2) to Lp(R2) for 1 < p ≤ ∞ . The authors prove that [Formula: see text] is bounded from L P ( R 2 ) to L P ( R 2 ) for 1 < p ≤ ∞. Euclidean harmonic analysis norm estimates THE AUTHORS PROVE THAT [FORMULA: see text] is bounded from L(P)(R(2)) to L(P)(R(2)) for 1 < p </= infinity. The authors prove that [Formula: see text] is bounded from L P ( R 2 ) to L P ( R 2 ) for 1 < p ≤ ∞. THE AUTHORS PROVE THAT [FORMULA: see text] is bounded from L(P)(R(2)) to L(P)(R(2)) for 1 < p </= infinity. |
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SubjectTerms | Mathematical integrals Mathematical theorems Physical Sciences: Mathematics |
Title | A Maximal Function Associated to the Curve (t, t2) |
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