In this paper, we first introduce some new classes of weighted amalgam spaces. Then, we give the weighted strong-type and weak-type estimates for fractional integral operators on these new function spaces. Furthermore, the weighted strong-type estimate and endpoint estimate of linear commutators generated by and are established as well. In addition, we are going to study related problems about two-weight, weak-type inequalities for and on the weighted amalgam spaces and give some results. Based on these results and pointwise domination, we can prove norm inequalities involving fractional maximal operator and generalized fractional integrals in the context of weighted amalgam spaces, where and is the infinitesimal generator of an analytic semigroup on with Gaussian kernel bounds.

中文翻译：

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某些加权汞合金空间上分数阶积分算子和线性交换子的估计

在本文中，我们首先介绍一些新的加权汞合金空间类别。然后，我们在这些新函数空间上给出了分数积分算子的加权强类型和弱类型估计。此外，线性换向器的加权强类型估计和终点估计通过产生和建立为好。此外，我们将研究关于相关问题的两个重量，弱型不等式和在加权的汞合金空间上给出一些结果。基于这些结果和逐点控制，我们可以证明在加权汞合金空间的情况下涉及分数最大算子和广义分数积分的范式不等式，其中并且是具有高斯核边界的解析半群的无穷小生成器。