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 inProceedings of the National Academy of Sciences - PNAS Vol. 73; no. 5; pp. 1416 - 1417
Main Authors Nagel, Alexander, Riviere, Nestor, Wainger, Stephen
Format Journal Article
LanguageEnglish
Published United States National Academy of Sciences of the United States of America 01.05.1976
National Acad Sciences
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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 ≤ ∞ .
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 &lt; p &lt;/= 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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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 &lt; p &lt;/= 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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http://www.pnas.org/content/73/5/1416.abstract
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