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

Xavier Tolsa

doi:10.1007/978-3-319-00596-6_11

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
Title of host publication	Progress in Mathematics
Pages	319-379
Number of pages	60
Volume	307
ISBN (Electronic)	2296-505X
DOIs	https://doi.org/10.1007/978-3-319-00596-6_11
Publication status	Published - 1 Jan 2014

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10.1007/978-3-319-00596-6_11

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title = "RBMO(μ) and H1atb(μ)",

abstract = "{\textcopyright} 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).",

author = "Xavier Tolsa",

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doi = "10.1007/978-3-319-00596-6_11",

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T1 - RBMO(μ) and H1atb(μ)

AU - Tolsa, Xavier

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N2 - © 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).

AB - © 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).

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M3 - Chapter

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VL - 307

SP - 319

EP - 379

BT - Progress in Mathematics

ER -

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

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