Abstract
Let μ be a doubling Radon measure in ℝd such that supp μ = \( {\mathbb{R}}^{d}\). A function \( f \in L_{loc}^{1}(\mu)\) is said to belong to BMO (μ) (the space of functions with bounded mean oscillation with respect to μ) if there exists some constant c 1 such that \( \sup_{Q}\frac{1}{{\mu}(Q)} \int_{Q} \mid{f}(x) - m_{Q}(f)\mid d{\mu}(x) \leq {c}_{1}\) where the supremum is taken over all the cubes \( Q \subset {\mathbb{R}}^{d} {\rm{and}} m_{Q}(f)\) stands for the mean of f over Q with respect to μ, i.e. \( m_{Q}(f) = \int_{Q} f d{\mu}/{\mu}(Q)\)
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© 2014 Springer International Publishing Switzerland
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Tolsa, X. (2014). RBMO (μ) and \( {H}_{atb}^{1}(\mu)\) . In: Analytic Capacity, the Cauchy Transform, and Non-homogeneous Calderón–Zygmund Theory. Progress in Mathematics, vol 307. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-00596-6_11
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DOI: https://doi.org/10.1007/978-3-319-00596-6_11
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Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-00595-9
Online ISBN: 978-3-319-00596-6
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