# 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

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topAimar, 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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- Pólya G., Szegö G., Problems and Theorems in Analysis, Volume I, Springer-Verlag, Berlin-Heidelberg-New York, 1972.
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- Aimar H., Harboure E., Iaffei B., Extensions of a theorem of Stein and Zygmund, preprint.

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