Some characterizations of upper doubling conditions on metric measure spaces

Tan, Chaoqiang; Li, Ji

doi:10.1002/mana.201400347

Cited by 3 publications

(2 citation statements)

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“…These metric measure spaces of non-homogeneous type include both metric measure spaces of homogeneous type and metric measure spaces equipped with non-doubling measures as special cases. We mention that several equivalent characterizations for the upper doubling condition were recently established by Tan and Li [36,37].…”

Section: Introductionmentioning

confidence: 97%

Boundedness of certain commutators over non-homogeneous metric measure spaces

Lin

Yang

2016

Anal.Math.Phys.

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Let (X , d, μ) be a metric measure space satisfying the so-called upper doubling condition and the geometrically doubling condition. Let T be a Calderón-Zygmund operator with kernel satisfying only the size condition and some Hörmander-type condition, and b ∈ RBMO(μ) (the regularized BMO space with the discrete coefficient). In this paper, the authors establish the boundedness of the commutator T b := bT − T b generated by T and b from the atomic Hardy space H 1 (μ) with the discrete coefficient into the weak Lebesgue space L 1, ∞ (μ). From this and an interpolation theorem for sublinear operators which is also proved in this paper, the authors further show that the commutator T b is bounded on L p (μ) for all p ∈ (1, ∞). Moreover, the boundedness of the commutator generated by the generalized fractional integral T α (α ∈ (0, 1)) and the RBMO(μ) function from H 1 (μ) into L 1/(1−α), ∞ (μ) is also presented.

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Section: Introductionmentioning

confidence: 97%

Boundedness of certain commutators over non-homogeneous metric measure spaces

Lin

Yang

2016

Anal.Math.Phys.

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“…If log dens E = log dens E = ε, say, for a set E, we say that E has logarithmic density ε. The doubling property [7] plays an important role in what follows.…”

Section: Introductionmentioning

confidence: 99%