Geodesic
Representation of the generalized Bessel potential by means of a Poisson kernel of the general form
Taurida Journal of Computer Science Theory and Mathematics, no. 1 (2022), pp. 40-52

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The article considers a generalization of the Poisson kernel, which in potential theory is an integral kernel used to simply represent the generalized Bessel potential as a one-dimensional integral and studies its properties. The concept of a common Poisson kernel is introduced. Further, it is shown that the generalized Bessel potential of a function integrable in the p-th degree with a power weight can be represented by an integral of a very simple form, using a Poisson kernel. Also in this paper, Young's inequality for B-convolutional operators in spaces $ \mathbf{B}_{\gamma}^{\alpha} $ is proved and some applications using the Laplace-Bessel differential operator are given. Generalized Poisson kernels find application in control theory and electrostatics problems.
Keywords: generalized Poisson kernel, Hankel transformation, generalized Bessel potential. 
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     author = {A. L. Dzhabrailov},
     title = {Representation of the generalized {Bessel} potential by means of a {Poisson} kernel of the general form},
     journal = {Taurida Journal of Computer Science Theory and Mathematics},
     pages = {40--52},
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A. L. Dzhabrailov. Representation of the generalized Bessel potential by means of a Poisson kernel of the general form. Taurida Journal of Computer Science Theory and Mathematics, no. 1 (2022), pp. 40-52. http://geodesic.mathdoc.fr/item/TVIM_2022_1_a3/