Two-weight norm inequalities for the fractional maximal operator on spaces of homogeneous type

Bernardis, Ana; Salinas, Oscar

Studia Mathematica, Tome 108 (1994), p. 201-207 / Harvested from The Polish Digital Mathematics Library

Résumé

We give a characterization of the pairs of weights (v,w), with w in the class $A_{\infty}$ of Muckenhoupt, for which the fractional maximal function is a bounded operator from $L^{p} (X, v d μ)$ to $L^{q} (X, w d μ)$ when 1 < p ≤ q < ∞ and X is a space of homogeneous type.

Publié le : 1994-01-01

Zbl 0846.42013

EUDML-ID : urn:eudml:doc:216050

@article{bwmeta1.element.bwnjournal-article-smv108i3p201bwm,
     author = {Ana Bernardis and Oscar Salinas},
     title = {Two-weight norm inequalities for the fractional maximal operator on spaces of homogeneous type},
     journal = {Studia Mathematica},
     volume = {108},
     year = {1994},
     pages = {201-207},
     zbl = {0846.42013},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv108i3p201bwm}
}

Bernardis, Ana; Salinas, Oscar. Two-weight norm inequalities for the fractional maximal operator on spaces of homogeneous type. Studia Mathematica, Tome 108 (1994) pp. 201-207. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv108i3p201bwm/

Bibliographie

[00000] [AM] H. Aimar and R. Macías, Weighted norm inequalities for the Hardy-Littlewood maximal operator on spaces of homogeneous type, Proc. Amer. Math. Soc. 91 (1984), 213-216. | Zbl 0539.42007

[00001] [C] A. Calderón, Inequalities for the maximal function relative to a metric, Studia Math. 57 (1976), 297-306. | Zbl 0341.44007

[00002] [CF] R. Coifman and C. Fefferman, Weighted norm inequalities for maximal functions and singular integrals, ibid. 51 (1974), 241-250. | Zbl 0291.44007

[00003] [CW] R. Coifman et G. Weiss, Analyse harmonique non-commutative sur certains espaces homogènes, Lecture Notes in Math. 242, Springer, Berlin, 1971.

[00004] [MS1] R. Macías and C. Segovia, Lipschitz functions on spaces of homogeneous type, Adv. in Math. 33 (1979), 257-270. | Zbl 0431.46018

[00005] [MS2] R. Macías and C. Segovia, A well behaved quasi-distance for spaces of homogeneous type, Trabajos de Matemática, no. 32, Inst. Argentino de Matemática, 1981.

[00006] [MT] R. Macías and J. L. Torrea, L² and $L^{p}$ boundedness of singular integrals on not necessarily normalized spaces of homogeneous type, Cuadernos de Matemática y Mecánica, PEMA-GTM-INTEC, no. 1-88, 1988.

[00007] [MW] B. Muckenhoupt and R. Wheeden, Weighted norm inequalities for fractional integrals, Trans. Amer. Math. Soc. 192 (1974), 261-274. | Zbl 0289.26010

[00008] [P] C. Perez, Two weighted norm inequalities for Riesz potentials and uniform $L^{p}$ -weighted Sobolev inequalities, Indiana Univ. Math. J. 39 (1990), 31-44. | Zbl 0736.42015

[00009] [SW] E. Sawyer and R. Wheeden, Weighted inequalities for fractional integrals on Euclidean and homogeneous spaces, Amer. J. Math. 114 (1992), 813-874. | Zbl 0783.42011

[00010] [W] R. Wheeden, A characterization of some weighted norm inequalities for the fractional maximal function, Studia Math. 107 (1993), 257-272. | Zbl 0809.42009