Two-weight norm inequalities for the fractional maximal operator on spaces of homogeneous type
Studia Mathematica (1994)
- Volume: 108, Issue: 3, page 201-207
- ISSN: 0039-3223
Access Full Article
top
Abstract
topHow to cite
topBernardis, Ana, and Salinas, Oscar. "Two-weight norm inequalities for the fractional maximal operator on spaces of homogeneous type." Studia Mathematica 108.3 (1994): 201-207. <http://eudml.org/doc/216050>.
@article{Bernardis1994,
abstract = {We give a characterization of the pairs of weights (v,w), with w in the class $A_∞$ of Muckenhoupt, for which the fractional maximal function is a bounded operator from $L^p(X,vdμ)$ to $L^q(X,wdμ)$ when 1 < p ≤ q < ∞ and X is a space of homogeneous type.},
author = {Bernardis, Ana, Salinas, Oscar},
journal = {Studia Mathematica},
keywords = {Muckenhoupt condition; Calderón-Zygmund decomposition; fractional maximal function; space of homogeneous type},
language = {eng},
number = {3},
pages = {201-207},
title = {Two-weight norm inequalities for the fractional maximal operator on spaces of homogeneous type},
url = {http://eudml.org/doc/216050},
volume = {108},
year = {1994},
}
TY - JOUR
AU - Bernardis, Ana
AU - Salinas, Oscar
TI - Two-weight norm inequalities for the fractional maximal operator on spaces of homogeneous type
JO - Studia Mathematica
PY - 1994
VL - 108
IS - 3
SP - 201
EP - 207
AB - We give a characterization of the pairs of weights (v,w), with w in the class $A_∞$ of Muckenhoupt, for which the fractional maximal function is a bounded operator from $L^p(X,vdμ)$ to $L^q(X,wdμ)$ when 1 < p ≤ q < ∞ and X is a space of homogeneous type.
LA - eng
KW - Muckenhoupt condition; Calderón-Zygmund decomposition; fractional maximal function; space of homogeneous type
UR - http://eudml.org/doc/216050
ER -
References
top- [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. Zbl0539.42007
- [C] A. Calderón, Inequalities for the maximal function relative to a metric, Studia Math. 57 (1976), 297-306. Zbl0341.44007
- [CF] R. Coifman and C. Fefferman, Weighted norm inequalities for maximal functions and singular integrals, ibid. 51 (1974), 241-250. Zbl0291.44007
- [CW] R. Coifman et G. Weiss, Analyse harmonique non-commutative sur certains espaces homogènes, Lecture Notes in Math. 242, Springer, Berlin, 1971.
- [MS1] R. Macías and C. Segovia, Lipschitz functions on spaces of homogeneous type, Adv. in Math. 33 (1979), 257-270. Zbl0431.46018
- [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.
- [MT] R. Macías and J. L. Torrea, L² and boundedness of singular integrals on not necessarily normalized spaces of homogeneous type, Cuadernos de Matemática y Mecánica, PEMA-GTM-INTEC, no. 1-88, 1988.
- [MW] B. Muckenhoupt and R. Wheeden, Weighted norm inequalities for fractional integrals, Trans. Amer. Math. Soc. 192 (1974), 261-274. Zbl0289.26010
- [P] C. Perez, Two weighted norm inequalities for Riesz potentials and uniform -weighted Sobolev inequalities, Indiana Univ. Math. J. 39 (1990), 31-44. Zbl0736.42015
- [SW] E. Sawyer and R. Wheeden, Weighted inequalities for fractional integrals on Euclidean and homogeneous spaces, Amer. J. Math. 114 (1992), 813-874. Zbl0783.42011
- [W] R. Wheeden, A characterization of some weighted norm inequalities for the fractional maximal function, Studia Math. 107 (1993), 257-272. Zbl0809.42009
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.