Geodesic
Nikol'skii--Besov and Lizorkin--Triebel spaces constructed on the base of the multidimensional Fourier--Bessel transform
Eurasian mathematical journal, Tome 2 (2011) no. 3, pp. 42-66

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In this paper we define the Nikol'skii–Besov and Lizorkin–Triebel spaces ($B$-Nikol'skii–Besov and $B$-Lizorkin–Triebel spaces) in the context of the Fourier–Bessel harmonic analysis. We establish some basic properties of the $B$-Nikol'skii–Besov and $B$-Lizorkin–Triebel spaces such as embedding theorems, the lifting property, and characterizing of the Bessel potentials in terms of the $B$-Lizorkin–Triebel spaces. We prove the inclusion and the density of the Schwartz space in the $B$-Nikol'skii–Besov and $B$-Lizorkin–Triebel spaces and prove an interpolation formula for these spaces by the real method. We also prove the Young inequality for the $B$-convolution operators in the $B$-Bessel potential spaces. Finally, we give some applications involving the Laplace–Bessel differential operator. 
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     author = {V. S. Guliyev and A. Serbetci and A. Akbulut and Y. Y. Mammadov},
     title = {Nikol'skii--Besov and {Lizorkin--Triebel} spaces constructed on the base of the multidimensional {Fourier--Bessel} transform},
     journal = {Eurasian mathematical journal},
     pages = {42--66},
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V. S. Guliyev; A. Serbetci; A. Akbulut; Y. Y. Mammadov. Nikol'skii--Besov and Lizorkin--Triebel spaces constructed on the base of the multidimensional Fourier--Bessel transform. Eurasian mathematical journal, Tome 2 (2011) no. 3, pp. 42-66. http://geodesic.mathdoc.fr/item/EMJ_2011_2_3_a2/