Abstract

We investigate the properties of spaces with generalized smoothness, such as Calderón spaces, that include the classical Nikolskii–Besov spaces and many of their generalizations, and describe differential properties of generalized Bessel potentials that include classical Bessel potentials and Sobolev spaces. The kernels of potentials may have non-power singularities at the origin. Using order-sharp estimates for the moduli of continuity of potentials, we establish criteria for the embeddings of potentials into Calderón spaces and describe the optimal spaces for such embeddings.

中文翻译：

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广义贝塞尔势的最佳Calderón空间

摘要

我们研究了具有广义光滑度的空间的属性，例如Calderón空间，其中包括经典的Nikolskii–Besov空间及其许多泛化，并描述了包括经典Bessel势和Sobolev空间的广义Bessel势的微分性质。势能的核在原点可能具有非幂奇异性。使用针对电位连续性模量的阶次锐角估计，我们建立了将电位嵌入Calderón空间的标准，并描述了此类嵌入的最佳空间。