Generalized Riesz B-potentials of the mixed type

Theory of generalized Bessel potential space and functional completion

“…γ can be determined in the sense of weighted generalized functions. As a consequence of this fact in [22] (see Theorem 5), it was proved that • C ∞ ev is dense in the space of Riesz B-potentials only for 0<α< n+|γ | p . So the norm based on Riesz B-potential is not convenient for using in the differential problems, because for these problems we need potentials of arbitrarily high order.…”

“…From a practical and theoretical point of view, it is important to establish in what the space and with what norm the set • C ∞ ev is dense. In [22], the space of functions related to multiplication by |x| −α in the images of Hankel transform was introduced and considered. This space is called the Riesz Bpotential space.…”

Weighted generalized functions and hyperbolic Riesz B‐potential

“…The method of construction of a new transmutation operator by (24) is the particular case of the composition method developed in previous studies. [37][38][39] For the approach to study transmutations operators connected with Bessel operator, see other studies.…”

“…[15][16][17][18][19][20] Riesz B-potential with Euclidean distance in the weighted Lebegue spaces and its inverse are given in references herein. [21][22][23][24][25][26][27] In Sarikaya et al, 28 for the operator similar to operator (3), some properties other than given in this article were obtained. The operator (3) and the corresponding integral kernels were studied in recent works.…”

“…Sobolev theorems for potential generated by Bessel operator with Euclidean distance in the Morrey‐Bessel and BMO‐Bessel spaces were considered in previous studies . Riesz B‐potential with Euclidean distance in the weighted Lebegue spaces and its inverse are given in references herein . In Sarikaya et al, for the operator similar to operator , some properties other than given in this article were obtained.…”