Abstract:
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 BLizorkin-
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 BBessel
potential spaces. Finally, we give some applications involving the Laplace-Bessel
differential operator.
