关于Calderón-Zygmund算子的熵颠簸

IF 0.3 Q4 MATHEMATICS Concrete Operators Pub Date : 2015-04-11 DOI:10.1515/conop-2015-0003

M. Lacey, Scott Spencer

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引用次数: 16

摘要

摘要:我们研究了Treil-Volberg最近提出的“熵”这一创新语言中的两个权不等式。对1 < p≠2 <∞的不等式推广到Lp，并给出了新的简短证明。证明结果如下:设(1，∞)上的一个单调递增函数，满足σ和w是两个权值。如果这个上极值是有限的，对于1 < p <∞的选择，则任意Calderón-Zygmund算子T满足||Tof||Lp(w) > ||f|| Lp(o)。

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On Entropy Bumps for Calderón-Zygmund Operators

Abstract We study twoweight inequalities in the recent innovative language of ‘entropy’ due to Treil-Volberg. The inequalities are extended to Lp, for 1 < p ≠ 2 < ∞, with new short proofs. A result proved is as follows. Let ɛ be a monotonic increasing function on (1,∞) which satisfy Let σ and w be two weights on ℝd. If this supremum is finite, for a choice of 1 < p < ∞, then any Calderón-Zygmund operator T satisfies the bound ||Tof||Lp(w) ≲ ||f|| Lp(o).

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