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2019•arXiv (Cornell University)Open access

On the compactness of oscillation and variation of commutators

Weichao Guo, Yongming Wen, Huoxiong Wu, Dongyong Yang

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Abstract

In this paper, we first establish the weighted compactness result for oscillation and variation associated with the truncated commutator of singular integral operators. Moreover, we establish a new $CMO(\mathbb{R}^n)$ characterization via the compactness of oscillation and variation of commutators on weighted Lebesgue spaces.

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What this paper is about

In this paper, we first establish the weighted compactness result for oscillation and variation associated with the truncated commutator of singular integral operators. Moreover, we establish a new $CMO(\mathbb{R}^n)$ characterization via the compactness of oscillation and variation of commutators on weighted Lebesgue spaces.

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Available abstract

In this paper, we first establish the weighted compactness result for oscillation and variation associated with the truncated commutator of singular integral operators. Moreover, we establish a new $CMO(\mathbb{R}^n)$ characterization via the compactness of oscillation and variation of commutators on weighted Lebesgue spaces.

Key concepts: Commutator, Compact space, Oscillation (cell signaling), Mathematics, Pure mathematics, Characterization (materials science), Lebesgue integration, Variation (astronomy)

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