Weighted inequalities for commutators of fractional integrals on spaces of homogeneous type |
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Authors: | Ana Bernardis Silvia Hartzstein |
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Institution: | a IMAL-CONICET, Güemes 3450, (3000) Santa Fe, Argentina b Facultad de Ingeniería Química, Universidad Nacional del Litoral, Santiago del Estero 2829, (3000) Santa Fe, Argentina |
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Abstract: | Let 0<γ<1, b be a BMO function and the commutator of order m for the fractional integral. We prove two type of weighted Lp inequalities for in the context of the spaces of homogeneous type. The first one establishes that, for A∞ weights, the operator is bounded in the weighted Lp norm by the maximal operator Mγ(Mm), where Mγ is the fractional maximal operator and Mm is the Hardy-Littlewood maximal operator iterated m times. The second inequality is a consequence of the first one and shows that the operator is bounded from to , where (m+1)p] is the integer part of (m+1)p and no condition on the weight w is required. From the first inequality we also obtain weighted Lp-Lq estimates for generalizing the classical results of Muckenhoupt and Wheeden for the fractional integral operator. |
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Keywords: | Commutators Fractional integral Spaces of homogeneous type Weighted strong inequalities |
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