On maximal functions over circular sectors with rotation invariant measures

Hugo A. Aimar; Liliana Forzani; Virginia Naibo

Commentationes Mathematicae Universitatis Carolinae (2001)

  • Volume: 42, Issue: 2, page 311-318
  • ISSN: 0010-2628

Abstract

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Given a rotation invariant measure in ℝ n , we define the maximal operator over circular sectors. We prove that it is of strong type ( p , p ) for p > 1 and we give necessary and sufficient conditions on the measure for the weak type ( 1 , 1 ) inequality. Actually we work in a more general setting containing the above and other situations.

How to cite

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Aimar, Hugo A., Forzani, Liliana, and Naibo, Virginia. "On maximal functions over circular sectors with rotation invariant measures." Commentationes Mathematicae Universitatis Carolinae 42.2 (2001): 311-318. <http://eudml.org/doc/248809>.

@article{Aimar2001,
abstract = {Given a rotation invariant measure in $\mathbb \{R\}^n$, we define the maximal operator over circular sectors. We prove that it is of strong type $(p,p)$ for $p>1$ and we give necessary and sufficient conditions on the measure for the weak type $(1,1)$ inequality. Actually we work in a more general setting containing the above and other situations.},
author = {Aimar, Hugo A., Forzani, Liliana, Naibo, Virginia},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {maximal functions; spaces of homogeneous type; maximal functions; circular sectors; rotation invariant measures; spaces of homogeneous type},
language = {eng},
number = {2},
pages = {311-318},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On maximal functions over circular sectors with rotation invariant measures},
url = {http://eudml.org/doc/248809},
volume = {42},
year = {2001},
}

TY - JOUR
AU - Aimar, Hugo A.
AU - Forzani, Liliana
AU - Naibo, Virginia
TI - On maximal functions over circular sectors with rotation invariant measures
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2001
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 42
IS - 2
SP - 311
EP - 318
AB - Given a rotation invariant measure in $\mathbb {R}^n$, we define the maximal operator over circular sectors. We prove that it is of strong type $(p,p)$ for $p>1$ and we give necessary and sufficient conditions on the measure for the weak type $(1,1)$ inequality. Actually we work in a more general setting containing the above and other situations.
LA - eng
KW - maximal functions; spaces of homogeneous type; maximal functions; circular sectors; rotation invariant measures; spaces of homogeneous type
UR - http://eudml.org/doc/248809
ER -

References

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  1. Sjögren P., A remark on the maximal functions for measures in ℝ n , Amer. J. Math. 105 (1983), 1231-1233. (1983) MR0714775
  2. Coifman R., Weiss G., Analyse harmonique non-commutative sur certains espaces homogènes, étude de certaines intégrales singulières, Lectures Notes in Math., Vol 242, Springer-Verlag, 1971. Zbl0224.43006MR0499948
  3. Pólya G., Szegö G., Problems and Theorems in Analysis, Volume I, Springer-Verlag, Berlin-Heidelberg-New York, 1972. 
  4. de Guzmán M., Real Variable Methods in Fourier Analysis, North Holland, Amsterdam, 1981. MR0596037
  5. Macías R., Segovia C., Lipschitz functions on spaces of homogeneous type, Advances in Mathematics 33 (1979), 257-270. (1979) MR0546295
  6. Aimar H., Harboure E., Iaffei B., Extensions of a theorem of Stein and Zygmund, preprint. 

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