Geodesic
Weighted Generalized Hardy Inequalities for Nonincreasing Functions
Canadian journal of mathematics, Tome 43 (1991) no. 6, pp. 1121-1135

Voir la notice de l'article provenant de la source Cambridge University Press

The nonnegative weight function pairs u, v for which the operator maps the nonnegative nonincreasing functions in LP(v) boundedly into weak Lq(u) are characterized. This result is used, in particular, both to generalize and to provide an alternate proof of certain strong type inequalities recently obtained by Ariño and Muckenhouptfor the Hardy averaging operator restricted to nonnegative nonincreasing functions.
DOI : 10.4153/CJM-1991-065-9
Mots-clés : 26D15, 42B25, Weighted inequalities, weak type inequality, Hardy's inequality 
Andersen, Kenneth F. Weighted Generalized Hardy Inequalities for Nonincreasing Functions. Canadian journal of mathematics, Tome 43 (1991) no. 6, pp. 1121-1135. doi: 10.4153/CJM-1991-065-9
@article{10_4153_CJM_1991_065_9,
     author = {Andersen, Kenneth F.},
     title = {Weighted {Generalized} {Hardy} {Inequalities} for {Nonincreasing} {Functions}},
     journal = {Canadian journal of mathematics},
     pages = {1121--1135},
     year = {1991},
     volume = {43},
     number = {6},
     doi = {10.4153/CJM-1991-065-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1991-065-9/}
}
TY  - JOUR
AU  - Andersen, Kenneth F.
TI  - Weighted Generalized Hardy Inequalities for Nonincreasing Functions
JO  - Canadian journal of mathematics
PY  - 1991
SP  - 1121
EP  - 1135
VL  - 43
IS  - 6
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1991-065-9/
DO  - 10.4153/CJM-1991-065-9
ID  - 10_4153_CJM_1991_065_9
ER  - 
%0 Journal Article
%A Andersen, Kenneth F.
%T Weighted Generalized Hardy Inequalities for Nonincreasing Functions
%J Canadian journal of mathematics
%D 1991
%P 1121-1135
%V 43
%N 6
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1991-065-9/
%R 10.4153/CJM-1991-065-9
%F 10_4153_CJM_1991_065_9

[1] 1. Andersen, K.F., Weighted inequalities for the Stieltjes transformation and Hubert's double series, Proc. Roy. Soc. Edinburgh 86A(1980), 75–84. Google Scholar

[2] 2. Andersen, K.F. and Muckenhoupt, B., Weighted weak type Hardy inequalities with applications to Hilbert transforms and maximal functions, Studia Math. 72(1982), 9–26. Google Scholar

[3] 3. Ariño, M. and Muckenhoupt, B., Maximal functions on classical Lorentz spaces and Hardy's inequality with weights for noninc re asing functions, Trans. Amer. Math. Soc. 320(1990), 727–735. Google Scholar

[4] 4. Bennett, C. and Sharpley, R., Interpolation of Operators. Academic Press, Orlando, 1988. Google Scholar

[5] 5. Boyd, D.W., The Hilbert transform on rearrangement-invariant spaces, Canad. J. Math. 19(1967), 599–616. Google Scholar

[6] 6. Braverman, M. Sh., On a class of operators, preprint. Google Scholar

[7] 7. Lai, S., Weighted norm inequalities for general operators on monotone functions, preprint. Google Scholar

[8] 8. Lai, S., Weak and strong type inequalities with weights for general operators on monotone functions, preprint. Google Scholar

[9] 9. Maźja, V.G., Sobolev Spaces. Springer-Verlag, Berlin, 1985. Google Scholar

[10] 10. Neugebauer, C. J., Weightednorm inequalitiesfor averaging operators ofmonotone functions, Publicationes Mathématiques, to appear. Google Scholar

[11] 11. Neugebauer, C. J., Some classical operators on Lorentz spaces, preprint. Google Scholar

[12] 12. Sawyer, E.T., Boundedness of classical operators on classical Lorentz spaces, Studia Math. 96(1990), 145–158. Google Scholar

[13] 13. Stepanov, V.D., The weighted Hardy's inequality for nonincreasing functions, Trans. Amer. Math. Soc. (to appear). Google Scholar

Cité par Sources :