# 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

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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
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- [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.
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- [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 ${L}^{p}$ boundedness of singular integrals on not necessarily normalized spaces of homogeneous type, Cuadernos de Matemática y Mecánica, PEMA-GTM-INTEC, no. 1-88, 1988.
- [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 ${L}^{p}$-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

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