In this paper we give a unified treatment of multidimensional fractal Hilbert-type inequalities. More precisely, we establish a Hilbert-type inequality with a general local fractional continuous kernel and weight functions. A particular emphasis is dedicated to a class of inequalities with a homogeneous kernel. Namely, we impose some weak conditions for which the constants appearing on the right-hand sides of such Hilbert-type inequalities are the best possible. As an application, we discuss some particular choices of homogeneous kernels and power weight functions.

中文翻译：

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通过局部分数演算获得的多维希尔伯特型不等式

在本文中，我们对多维分形希尔伯特型不等式进行统一处理。更准确地说，我们建立了具有一般局部分数连续核和权函数的希尔伯特型不等式。特别强调的是一类具有齐次核的不等式。即，我们强加一些弱条件，对于这些条件，出现在这种希尔伯特型不等式右侧的常数是最好的。作为应用程序，我们讨论均质内核和功率权重函数的一些特定选择。