Weighted inequalities for commutators of fractional integrals on spaces of homogeneous type
- Bernardis, Ana
- Hartzstein, Silvia
- Pradolini, Gladis
DOIAbstract
AbstractLet 0<γ<1, b be a BMO function and Iγ,bm the commutator of order m for the fractional integral. We prove two type of weighted Lp inequalities for Iγ,bm in the context of the spaces of homogeneous type. The first one establishes that, for A∞ weights, the operator Iγ,bm 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 Iγ,bm is bounded from Lp[Mγp(M[(m+1)p]w)(x)dμ(x)] to Lp[w(x)dμ(x)], 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–...
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