Ideal weights: Asymptotically optimal versions of doubling, absolute continuity, and bounded mean oscillation
Ideal weights: Asymptotically optimal versions of doubling, absolute continuity, and bounded mean oscillation
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理想权重：加倍、绝对连续性和有界平均振荡的渐近最优版本
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发表时间：
1998
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通讯作者：
M. Korey
中科院分区：
文献类型：
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作者：
M. Korey
尖锐的不平等之间的重量界（从加倍，Ap，和反向Hölder条件）和BMO范数时，前者是接近其最佳值。特别地，权重的对数的BMO范数由其A∞界的对数的平方根控制。这些估计导致了系统地发展了反向Hölder权的渐近尖锐的更高可积性结果，并将Coifman和February man关于A∞条件的公式作为加倍测度的等价关系扩展到所有边界在小尺度上都变得最优的设置。
Sharp inequalities between weight bounds (from the doubling, Ap, and reverse Hölder conditions) and the BMO norm are obtained when the former are near their optimal values. In particular, the BMO norm of the logarithm of a weight is controlled by the square root of the logarithm of its A∞ bound. These estimates lead to a systematic development of asymptotically sharp higher integrability results for reverse Hölder weights and extend Coifman and Fefferman's formulation of the A∞ condition as an equivalence relation on doubling measures to the setting in which all bounds become optimal over small scales.