Compact Commutators of Rough Singular Integral Operators
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Bibliographic record
Abstract
Abstract Let b ∊ BMO(ℝ n ) and T Ω be the singular integral operator with kernel Ω( x )/| x | n , where Ω is homogeneous of degree zero, integrable, and has mean value zero on the unit sphere S n-1 . In this paper, using Fourier transform estimates and approximation to the operator T Ω by integral operators with smooth kernels, it is proved that if b ∊ CMO(ℝ n ) and satisfies certain minimal size condition, then the commutator generated by b and T Ω is a compact operator on L p (ℝ n ) for appropriate index p . The associated maximal operator is also considered.
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Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.013 | 0.002 |
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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