Modular inequalities for the Hardy averaging operator
Mathematica Bohemica (1999)
- Volume: 124, Issue: 2-3, page 231-244
- ISSN: 0862-7959
Access Full Article
top
Abstract
topHow to cite
topHeinig, Hans P.. "Modular inequalities for the Hardy averaging operator." Mathematica Bohemica 124.2-3 (1999): 231-244. <http://eudml.org/doc/248456>.
@article{Heinig1999,
abstract = {If $P$ is the Hardy averaging operator - or some of its generalizations, then weighted modular inequalities of the form
u (Pf) Cv (f)
are established for a general class of functions $\phi $. Modular inequalities for the two- and higher dimensional Hardy averaging operator are also given.},
author = {Heinig, Hans P.},
journal = {Mathematica Bohemica},
keywords = {Hardy inequality; modular inequality; weight functions; Hardy inequality; modular inequality; weight functions},
language = {eng},
number = {2-3},
pages = {231-244},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Modular inequalities for the Hardy averaging operator},
url = {http://eudml.org/doc/248456},
volume = {124},
year = {1999},
}
TY - JOUR
AU - Heinig, Hans P.
TI - Modular inequalities for the Hardy averaging operator
JO - Mathematica Bohemica
PY - 1999
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 124
IS - 2-3
SP - 231
EP - 244
AB - If $P$ is the Hardy averaging operator - or some of its generalizations, then weighted modular inequalities of the form
u (Pf) Cv (f)
are established for a general class of functions $\phi $. Modular inequalities for the two- and higher dimensional Hardy averaging operator are also given.
LA - eng
KW - Hardy inequality; modular inequality; weight functions; Hardy inequality; modular inequality; weight functions
UR - http://eudml.org/doc/248456
ER -
References
top- Maria J. Carro, Hans Heinig, Modular inequalities for the Calderón operator, Tohoku Math. J. To appear. MR1740541
- M. DeGuzmán, Real Variable Methods in Fourier analysis, Univ. Complutense de Madrid, Fac. Mat., 1977. (1977)
- P. Drábek H. P. Heinig A. Kufner, Higher dimensional Hardy inequality, Internat. Ser. Numer. Math. 123 (1997), 3-16. (1997) MR1457264
- G. H. Hardy J. E. Littlewood G. Pólya, Inequalities, Cambridge, 1934. (1934) MR0046395
- H. P. Heinig R. Kerman M. Krbec, Weighted exponential inequalities, Preprint, vol. 79, Math. Inst., Acad. Science, Praha, 1992, pp. 30. (1992) MR1828685
- Hans P. Heinig, Qinsheng Lai, Weighted modular inequalities for Hardy-type operators on monotone functions, Preprint. MR1756661
- Qinsheng Lai, Weighted modular inequalities for Hardy-type operators, J. London Math. Soc. To appear. MR1710168
- N. Levinson, 10.1215/S0012-7094-64-03137-0, Duke J. Math. 31 (1964), 389-394. (1964) Zbl0126.28101MR0171885DOI10.1215/S0012-7094-64-03137-0
- B. Opic A. Kufner, Hardy type inequalities, Pitman Series 219, Harlow, 1990. (1990) MR1069756
- B. Opic P. Gurka, 10.1090/S0002-9939-1994-1169043-4, Proc. Arner. Math. Soc. 120 (1994), no. 3, 771-779. (1994) MR1169043DOI10.1090/S0002-9939-1994-1169043-4
- E. Sawyer, 10.4064/sm-82-1-1-16, Studia Math. 82 (1985), 1-16. (1985) Zbl0585.42020MR0809769DOI10.4064/sm-82-1-1-16
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.