RBMO(μ) and H<sup>1</sup><inf>atb</inf>(μ)

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Abstract

© Springer International Publishing Switzerland 2014. Let μ be a doubling Radon measure in ℝd such that supp μ = ℝd. A function f ∈ L1loc(μ) is said to belong to BMO(μ) (the space of functions with bounded mean oscillation with respect to μ) if there exists some constant c1 such that {Formula presented}, where the supremum is taken over all the cubes Q ⊂ ℝd and mQ(f) stands for the mean of f over Q with respect to μ, i.e. mQ(f) = ∫ Q f dμ/μ(Q).
Original language English Progress in Mathematics 319-379 60 307 2296-505X https://doi.org/10.1007/978-3-319-00596-6_11 Published - 1 Jan 2014