Commutators of singular K-pseudodifferential operators in Rn.

To study problems with the Kipriyanov singular differential operator Δ B - γ with a negative parameter - γ ∈ (- 1 , 0) , an integral transformation is introduced in the work, based on the solution u = J μ of the singular Bessel equation B - γ u + u = 0 . This solution is expressed through a Bessel function of the first kind with a positive parameter μ = γ + 1 2 . An even, odd and complete FBK transform (Fourier—Bessel—Kipriyanov—Katrakhov transform) and a class of singular K -pseudodifferential operators are constructed. Theorems on the order and commutator of singular K -pseudodifferential operators are obtained. [ABSTRACT FROM AUTHOR]