| Title:
|
On maximal functions over circular sectors with rotation invariant measures (English) |
| Author:
|
Aimar, H. |
| Author:
|
Forzani, L. |
| Author:
|
Naibo, V. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
42 |
| Issue:
|
2 |
| Year:
|
2001 |
| Pages:
|
311-318 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Given a rotation invariant measure in $\Bbb R^n$, 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. (English) |
| Keyword:
|
maximal functions |
| Keyword:
|
spaces of homogeneous type |
| MSC:
|
42B25 |
| MSC:
|
43A85 |
| idZBL:
|
Zbl 1054.42014 |
| idMR:
|
MR1832149 |
| . |
| Date available:
|
2009-01-08T19:10:05Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119245 |
| . |
| Reference:
|
[1] Sjögren P.: A remark on the maximal functions for measures in $\Bbb R^n$.Amer. J. Math. 105 (1983), 1231-1233. MR 0714775 |
| Reference:
|
[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. Zbl 0224.43006, MR 0499948 |
| Reference:
|
[3] Pólya G., Szegö G.: Problems and Theorems in Analysis.Volume I, Springer-Verlag, Berlin-Heidelberg-New York, 1972. |
| Reference:
|
[4] de Guzmán M.: Real Variable Methods in Fourier Analysis.North Holland, Amsterdam, 1981. MR 0596037 |
| Reference:
|
[5] Macías R., Segovia C.: Lipschitz functions on spaces of homogeneous type.Advances in Mathematics 33 (1979), 257-270. MR 0546295 |
| Reference:
|
[6] Aimar H., Harboure E., Iaffei B.: Extensions of a theorem of Stein and Zygmund.preprint. |
| . |
