| Title:
|
Modular inequalities for the Hardy averaging operator (English) |
| Author:
|
Heinig, Hans P. |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
124 |
| Issue:
|
2 |
| Year:
|
1999 |
| Pages:
|
231-244 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
If $P$ is the Hardy averaging operator - or some of its generalizations, then weighted modular inequalities of the form
\int u \phi(Pf) \leq C\int v \phi(f)
are established for a general class of functions $\phi$. Modular inequalities for the two- and higher dimensional Hardy averaging operator are also given. (English) |
| Keyword:
|
Hardy inequality |
| Keyword:
|
modular inequality |
| Keyword:
|
weight functions |
| MSC:
|
26A33 |
| MSC:
|
26D05 |
| MSC:
|
26D15 |
| MSC:
|
46E30 |
| MSC:
|
46M35 |
| idZBL:
|
Zbl 0936.26006 |
| idMR:
|
MR1780694 |
| DOI:
|
10.21136/MB.1999.126254 |
| . |
| Date available:
|
2009-09-24T21:37:31Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/126254 |
| . |
| Reference:
|
[1] Maria J. Carro, Hans Heinig: Modular inequalities for the Calderón operator.Tohoku Math. J. To appear. MR 1740541 |
| Reference:
|
[2] M. DeGuzmán: Real Variable Methods in Fourier analysis.Univ. Complutense de Madrid, Fac. Mat., 1977. |
| Reference:
|
[3] P. Drábek H. P. Heinig A. Kufner: Higher dimensional Hardy inequality.Internat. Ser. Numer. Math. 123 (1997), 3-16. MR 1457264 |
| Reference:
|
[4] G. H. Hardy J. E. Littlewood G. Pólya: Inequalities.Cambridge, 1934. MR 0046395 |
| Reference:
|
[5] H. P. Heinig R. Kerman M. Krbec: Weighted exponential inequalities.Preprint, vol. 79, Math. Inst., Acad. Science, Praha, 1992, pp. 30. MR 1828685 |
| Reference:
|
[6] Hans P. Heinig, Qinsheng Lai: Weighted modular inequalities for Hardy-type operators on monotone functions.Preprint. MR 1756661 |
| Reference:
|
[7] Qinsheng Lai: Weighted modular inequalities for Hardy-type operators.J. London Math. Soc. To appear. MR 1710168 |
| Reference:
|
[8] N. Levinson: Generalizations of an inequality of Hardy.Duke J. Math. 31 (1964), 389-394. Zbl 0126.28101, MR 0171885, 10.1215/S0012-7094-64-03137-0 |
| Reference:
|
[9] B. Opic A. Kufner: Hardy type inequalities.Pitman Series 219, Harlow, 1990. MR 1069756 |
| Reference:
|
[10] B. Opic P. Gurka: Weighted inequalities for geometric means.Proc. Arner. Math. Soc. 120 (1994), no. 3, 771-779. MR 1169043, 10.1090/S0002-9939-1994-1169043-4 |
| Reference:
|
[11] E. Sawyer: Weighted inequalities for the two dimensional Hardy operator.Studia Math. 82 (1985), 1-16. Zbl 0585.42020, MR 0809769, 10.4064/sm-82-1-1-16 |
| . |
