Abstract We show that integrability properties of integral transforms with kernel depending on the product of arguments (which include in particular, popular Laplace, Hankel, Mittag-Leffler transforms and various others) are better described in terms of Morrey spaces than in terms of Lebesgue spaces. Mapping properties of integral transforms of such a type in Lebesgue spaces, including weight setting, are known. We discover that local weighted Morrey and complementary Morrey spaces are very appropriate spaces for describing integrability properties of such transforms. More precisely, we show that under certain natural assumptions on the kernel, transforms under consideration act from local weighted Morrey space to a weighted complementary Morrey space and vice versa, where an interplay between behavior of functions and their transforms at the origin and infinity is transparent. In case of multidimensional integral transforms, for this goal we introduce and use anisotropic mixed norm Morrey and complementary Morrey spaces.

中文翻译：

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通过莫雷空间积分变换的可积性

摘要 我们表明，根据参数的乘积（特别包括流行的拉普拉斯、汉克尔、米塔格-莱夫勒变换和其他各种变换）的核积分变换的可积性属性用莫雷空间比用勒贝格空间更好地描述. 勒贝格空间中这种类型的积分变换的映射性质，包括权重设置，是已知的。我们发现局部加权莫雷空间和互补莫雷空间是非常适合描述此类变换的可积性属性的空间。更准确地说，我们表明，在核的某些自然假设下，所考虑的变换从局部加权莫雷空间到加权互补莫雷空间，反之亦然，其中函数的行为与其在原点和无穷远处的变换之间的相互作用是透明的。在多维积分变换的情况下，为了这个目标，我们引入并使用各向异性混合范数 Morrey 和互补 Morrey 空间。