This paper establishes the Hardy–Littlewood–Pólya inequalities, the Hardy inequalities and the Hilbert inequalities on amalgam spaces. Moreover, it also gives the mapping properties of the Mellin convolutions, the Hadamard fractional integrals and the Hausdorff operators on amalgam spaces. We establish these properties by some estimates for the operator norms of the dilation operators on amalgam spaces.

中文翻译：

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汞合金空间上的膨胀算子和积分算子$$（L_ {p}，l_ {q}）$$（Lp，lq）

本文建立了汞齐空间上的Hardy-Littlewood-Pólya不等式，Hardy不等式和Hilbert不等式。此外，它还给出了汞合金空间上的梅林卷积，Hadamard分式积分和Hausdorff算符的映射性质。我们通过对汞合金空间上扩张算子的算子范数的一些估计来建立这些性质。