Geodesic
A + ∞ Condition
Canadian journal of mathematics, Tome 45 (1993) no. 6, pp. 1231-1244

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

The good weights for the one-sided Hardy-Littlewood operators have been characterized by conditions . In this paper we introduce a new condition which is analogous to A∞. We show several characterizations of . For example, we prove that the class of weights is the union of classes. We also give a new characterization of weights. Finally, as an application of condition, we characterize the weights for one-sided fractional integrals and one-sided fractional maximal operators.
DOI : 10.4153/CJM-1993-069-9
Mots-clés : 42B25, one-sided Hardy-Littlewood maximal operators, weighted inequalities, weights, one-sided fractional operators, one-sided fractional maximal operators, Riemann-Liouville fractional integral operator 
Martín-Reyes, F. J.; Pick, L.; Torre, A. De La. A + ∞ Condition. Canadian journal of mathematics, Tome 45 (1993) no. 6, pp. 1231-1244. doi: 10.4153/CJM-1993-069-9
@article{10_4153_CJM_1993_069_9,
     author = {Mart{\'\i}n-Reyes, F. J. and Pick, L. and Torre, A. De La},
     title = {A + \ensuremath{\infty} {Condition}},
     journal = {Canadian journal of mathematics},
     pages = {1231--1244},
     year = {1993},
     volume = {45},
     number = {6},
     doi = {10.4153/CJM-1993-069-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1993-069-9/}
}
TY  - JOUR
AU  - Martín-Reyes, F. J.
AU  - Pick, L.
AU  - Torre, A. De La
TI  - A + ∞ Condition
JO  - Canadian journal of mathematics
PY  - 1993
SP  - 1231
EP  - 1244
VL  - 45
IS  - 6
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1993-069-9/
DO  - 10.4153/CJM-1993-069-9
ID  - 10_4153_CJM_1993_069_9
ER  - 
%0 Journal Article
%A Martín-Reyes, F. J.
%A Pick, L.
%A Torre, A. De La
%T A + ∞ Condition
%J Canadian journal of mathematics
%D 1993
%P 1231-1244
%V 45
%N 6
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1993-069-9/
%R 10.4153/CJM-1993-069-9
%F 10_4153_CJM_1993_069_9

[AS] Andersen, K.F. and Sawyer, E.T., Weighted norm inequalities for the Riemann-Liouville and Weyl fractional integral operators, Trans. Amer. Math. Soc. 308(1988), 547–557. Google Scholar

[BK] Bagby, R.J. andKurtz, D.S., A rearranged good X-inequality, Trans. Amer. Math. Soc. 293(1986), 71–81. Google Scholar

[CF] Coifman, R.R. and Fefferman, C., Weighted norm inequalities for maximal functions and singular integrals, StudiaMath. 51(1974), 241–250. Google Scholar

[GR] Garcia-Cuerva, J. and de Francia, J.L. Rubio, Weighted norm inequalities and related topics, North- Holland, 1985. Google Scholar

[KT] Kerman, R.A. and Torchinsky, A., Integral inequalities with weights for the Hardy maximal function, Studia Math. 71(1982), 277–284. Google Scholar

[K] Kurtz, D.S., Better good X-inequalities, Miniconference on Harmonic Analysis and Operator Algebras Canberra 1987, Proc. Centre Math. Anal. Austral. Nat. Univ. 15, (1987), 118–130. Google Scholar

[M] Martin, F.J.-Reyes, New proofs of weighted inequalities for the one sided Hardy-Littlewood maximal functions, Proc. Amer. Math. Soc. 117(1993), 691–698. Google Scholar

[MOT] Martin, F.J.-Reyes, Salvador, P.Ortega and de la Torre, A. , Weighted inequalities for one-sided maximal functions, Trans. Amer. Math. Soc. 319-2(1990), 517–534. Google Scholar

[MT] Martin-Reyes, F.J. and de la Torre, A., Two weight norm inequalities for fractional one-sided maximal operators, Proc. Amer. Math. Soc. 117(1993), 483–489. Google Scholar

[MW] Muckenhouptand, B. Wheeden, R.L., Weighted norm inequalities for fractional integrals, Trans. Amer. Math. Soc. 192(1974), 261–274. Google Scholar

[Ol] Ortega, P., Weighted inequalities for one sided maximal functions in Orlicz spaces, Studia Math, to appear. Google Scholar

[O2] Ortega, P., Pesos para operadores maximales y teoremas ergodicos en espacios L, L y de Orlicz, Doctoral thesis, Universidad de Malaga, 1991. Google Scholar

[S] Sawyer, E., Weighted inequalities for the one sided Hardy-Litlewoodmaximalfunctions, Trans. Amer. Math. Soc. 297(1986), 53–61. Google Scholar

[St] Stein, E.M., Singular integrals and differentiability properties of functions, Princeton Univ. Press, Princeton N.J., 1970. Google Scholar

Cité par Sources :