Characterization of the Atomic Space H1 for Non Doubling Measures in Terms of a Grand Maximal Operator
نویسنده
چکیده
Let μ be a Radon measure on R, which may be non doubling. The only condition that μ must satisfy is the size condition μ(B(x, r)) ≤ C r, for some fixed 0 < n ≤ d. Recently, the author introduced spaces of type BMO(μ) and H(μ) with properties similar to ones of the classical spaces BMO and H defined for doubling measures. These new spaces proved to be useful to study the L(μ) boundedness of Calderón-Zygmund operators without assuming doubling conditions. In this paper a characterization of this new atomic Hardy space H(μ) in terms of a maximal operator MΦ is given. It is shown that f belongs to H(μ) if and only if f ∈ L(μ), ∫ f dμ = 0 and MΦf ∈ L (μ), as in the usual doubling situation.
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