The one-sided minimal operator and the one-sided reverse Holder inequality
Cruz-Uribe, David ; SFO ; Neugebauer, C. ; Olesen, V.
Studia Mathematica, Tome 113 (1995), p. 255-270 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

We introduce the one-sided minimal operator, m+f, which is analogous to the one-sided maximal operator. We determine the weight classes which govern its two-weight, strong and weak-type norm inequalities, and show that these two classes are the same. Then in the one-weight case we use this class to introduce a new one-sided reverse Hölder inequality which has several applications to one-sided (Ap+) weights.

Publié le : 1995-01-01
EUDML-ID : urn:eudml:doc:216232 
@article{bwmeta1.element.bwnjournal-article-smv116i3p255bwm,
     author = {David Cruz-Uribe and SFO and C. Neugebauer and V. Olesen},
     title = {The one-sided minimal operator and the one-sided reverse Holder inequality},
     journal = {Studia Mathematica},
     volume = {113},
     year = {1995},
     pages = {255-270},
     zbl = {0851.42017},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv116i3p255bwm}
}

Cruz-Uribe, David; SFO; Neugebauer, C.; Olesen, V. The one-sided minimal operator and the one-sided reverse Holder inequality. Studia Mathematica, Tome 113 (1995) pp. 255-270. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv116i3p255bwm/

[00000] [1] D. Cruz-Uribe, SFO, and C. J. Neugebauer, The structure of the reverse Hölder classes, Trans. Amer. Math. Soc. 347 (1995), 2941-2960. | Zbl 0851.42016

[00001] [2] D. Cruz-Uribe, SFO, C. J. Neugebauer and V. Olesen, Norm inequalities for the minimal and maximal operator, and differentiation of the integral, preprint. | Zbl 0903.42007

[00002] [3] J. García-Cuerva and J. L. Rubio de Francia, Weighted Norm Inequalities and Related Topics, North-Holland Math. Stud. 116, North-Holland, Amsterdam, 1985.

[00003] [4] G. H. Hardy and J. E. Littlewood, A maximal theorem with function-theoretic applications, Acta Math. 54 (1930), 81-116. | Zbl 56.0264.02

[00004] [5] F. J. Martín-Reyes, New proofs of weighted inequalities for the one-sided Hardy-Littlewood maximal functions, Proc. Amer. Math. Soc. 117 (1993), 691-698. | Zbl 0771.42011

[00005] [6] F. J. Martín-Reyes, P. Ortega Salvador and A. de la Torre, Weighted inequalities for one-sided maximal functions, Trans. Amer. Math. Soc. 319 (1990), 517-534. | Zbl 0696.42013

[00006] [7] F. J. Martín-Reyes, L. Pick and A. de la Torre, (A∞+) condition, Canad. J. Math. 45 (1993), 1231-1244. | Zbl 0797.42012

[00007] [8] F. J. Martín-Reyes and A. de la Torre, Two weight norm inequalities for fractional one-sided maximal operators, Proc. Amer. Math. Soc. 117 (1993), 483-489. | Zbl 0769.42010

[00008] [9] B. Muckenhoupt, Weighted norm inequalities for the Hardy maximal function, Trans. Amer. Math. Soc. 165 (1972), 207-226. | Zbl 0236.26016

[00009] [10] E. Sawyer, Weighted inequalities for the one sided Hardy-Littlewood maximal functions, ibid. 297 (1986), 53-61. | Zbl 0627.42009

[00010] [11] J. O. Strömberg and R. L. Wheeden, Fractional integrals on weighted Hp and Lp spaces, ibid. 287 (1985), 293-321.