Boundedness of pseudo-differential operator associated with fractional Hankel transform

Prasad, Akhilesh; Singh, V. K.

doi:10.2478/s13540-014-0160-x

Cited by 3 publications

(1 citation statement)

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“…Integral transforms of type (1.1) are well known to be widely used in various fields of mathematics, including fractional calculus, and various applications, with a variety of books on this topic. We refer, for instance, to the books [9], [10], [12], [13], [36], [40] and [48], articles [22], [27], [26], [28], [37], [44], [46], [47] and references therein. Integral transforms of such a type are well known to be used in the study of differential equations of fractional order, see for instance [5].…”

Section: Introductionmentioning

confidence: 99%

Integrability Properties of Integral Transforms Via Morrey Spaces

Samko

2020

Fract Calc Appl Anal

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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.

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