奇异积分算子两个权不等式中的熵条件
Entropy conditions in two weight inequalities for singular integral operators
摘要：
介绍了Muckenhoupt $A_2$条件在权上的一种新的“碰撞”.它是基于碰撞的熵积分的权重。特别地，人们得到（假设相应的杨函数上有温和的正则性条件）凸块猜想，这是A. Lerner和独立的Nazarov-Reznikov-Treil-Volberg，作为熵碰撞的必然结果。但我们的熵凸块不能简化为凸块猜想解中的Orlicz范数凸块，它们实际上更小。尽管如此，我们得到了比解决bump猜想的结果更强的结果。得到了关于单侧碰撞猜想的新结果。所有结果在一般非齐次情形下都成立。
英文摘要：
The new type of "bumping" of the Muckenhoupt $A_2$ condition on weights is introduced. It is based on bumping the entropy integral of the weights. In particular, one gets (assuming mild regularity conditions on the corresponding Young functions) the bump conjecture, proved earlier by A. Lerner and independently by Nazarov--Reznikov--Treil--Volberg, as a corollary of entropy bumping. But our entropy bumps cannot be reduced to the bumping with Orlicz norms in the solution of bump conjecture, they are effectively smaller. Henceforth we get somewhat stronger result than the one that solves the bump conjecture. New results concerning one sided bumping conjecture are obtained. All the results hold in the general non-homogeneous situation.
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