Pseudo-Differential Operators Involving Hankel Transforms

Two versions of pseudo-differential operators involving the Kontorovich–Lebedev transform in L 2(ℝ+;dx/x)

“…Some pseudo-differential operators associated with other integral transformations like Hankel transformations, Fourier-Jacobi transformations etc. are defined and their properties are discussed in [13,15,16,21]. Motivated by the works of Zaidman [31] and Pathak and Upadhyay [15], we define the pseudo-differential operator…”

Composition of pseudodifferential operators associated with fractional Hankel–Clifford integral transformations

“…Based on [12], in this paper, pdo h θ 1,ν,μ,a , h θ 2,ν,μ,a and h θ 1,ν,μ,b , h θ 2,ν,μ,b are defined by means of symbols a θ 1 (x, ξ), a θ 2 (x, ξ) and b θ 1 (y, η), b θ 2 (y, η), respectively, which are assumed to be the inverse fractional Hankel-Clifford integral transformations of functions V (λ, ξ ) and W (β, η) satisfying certain boundedness conditions. Compositions of pdo are defined.…”

Lp-Norm inequality of the product of pseudo-differential operators involving Hankel transformation

“…Motivated from [3] and [11], Pathak and Upadhyay [7] defined pseudo-differential operators Lðx, DÞ and Hðx, DÞ involving Hankel transformation and studied their various properties, where the operator Lðx, DÞ is an adjoint of Hðx, DÞ and Hðx, DÞ is a generalization of p.d.o. h , ' 0 which was studied in [5].…”

“…The notations and terminology of [7] and [14] are used in this article. Some formulae related to this article are given below: We shall make use of the following norm for 1 p < 1: where the function GðÞ is given by…”