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A NOTE ON WEIGHTED NORM INEQUALITIES FOR FRACTIONAL MAXIMAL OPERATORS WITH NON-DOUBLING MEASURES

Weihong Wang, Chaoqiang Tan and Zengjian Lou
Taiwanese Journal of Mathematics
Vol. 16, No. 4 (August 2012), pp. 1409-1422
Stable URL: http://www.jstor.org/stable/taiwjmath.16.4.1409
Page Count: 14
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A NOTE ON WEIGHTED NORM INEQUALITIES FOR FRACTIONAL MAXIMAL OPERATORS WITH NON-DOUBLING MEASURES
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Abstract

Abstract Let μ be a non-negative Borel measure on ℝd which only satisfies some growth condition, we study two-weight norm inequalities for fractional maximal functions associated to such μ. A necessary and sufficient condition for the maximal operator to be bounded from LP(v) into weak Lq(u) (1 ≤ p ≤ q < ∞) is given. Furthermore, by using certain Orlicz norm, a strong type inequality is obtained. 2010 Mathematics Subject Classification: 42B25. Key words and phrases: Non-homogeneous spaces, Fractional maximal operators, Muckenhoupt weights.

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