We study continuity properties for commutators of Calderón-Zygmund and fractional integral operators between generalized Zygmund spaces of L log L type, in the variable exponent setting with different weights. In order to reach this goal we use two different approaches: the first one is related to generalized bump conditions on a pair of weights, allowing us to handle with a wide class of symbol involved with the commutator. The other approaches give Bloom type estimates restricting the class of symbols. The techniques involved in both type of results are related with the theory of sparse domination.

中文翻译：

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稀疏算子对广义Zygmund空间上Calderón-Zygmund和分数积分算子的交换子的Musielak-Orlicz-凸点和Bloom类型估计

在具有不同权重的可变指数设置下，我们研究了Calderón-Zygmund交换子和L log L型广义Zygmund空间之间的分数积分算子的连续性。为了实现此目标，我们使用两种不同的方法：第一种方法与一对配重上的广义碰撞条件有关，从而使我们能够处理与换向器有关的各种符号。其他方法给出Bloom类型估计值，从而限制符号的类别。两种结果都涉及的技术与稀疏控制理论有关。