Abstract
Let μ be a Borel measure on ℝd which may be non doubling. The only condition that μ must satisfy is μ(Q)≤c0l(Q)n for any cubeQ ⊂ ℝd with sides parallel to the coordinate axes and for some fixed n with 0 < n ≤d. The purpose of this paper is to obtain a boundedness property of fractional integrals in Hardy spaces H1(μ).
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