A Pair of Pseudo-differential Operators Involving Index Whittaker Transform in L_(2)^(a) (R_(+);m_(a)(x)dx)

Pseudo-differential operators(PDO)Q(x,L_(a,x))and Q(x,L_(a,x))involving the index Whittaker transform are defined.Estimates for these operators in Hilbert space L_(2)^(a)(R+;m_(a)(x)dx)are obtained.A symbol classΩis introduced.Later product and commutators for the PDO are investigated and their boundedness results are discussed.

On the Sobolev Boundedness Results of the Product of Pseudo-differential Operators Involving a Couple of Fractional Hankel Transforms

This article is concerned with the study of pseudo-differential operators associated with fractional Hankel transform. The product of two fractional pseudo-differential operators is defined and investigated its basic properties on some function space. It is shown that the pseudo-differential operators and their products are bounded in Sobolev type spaces. Particular cases are discussed.

Fractional Wavelet Packet Transformations Involving Hankel–Clifford Integral Transformations

In this paper, we introduce the fractional wavelet transformations （FrWT） involving Han- kel-Clifford integral transformation （HCIIT） on the positive half line and studied some of its basic properties. Also we obtain Parseval＇s relation and an inversion formula. Examples of fractional powers of Hankel-Clifford integral transformation （FrHClIT） and FrWT are given. Then, we introduce the concept of fractional wavelet packet transformations FrBWPT and FrWPIT, and investigate their properties.

Product and Commutators of Pseudo-differential Operators Involving Fourier–Jacobi Transform

The purpose of this paper is to define a new symbol classand discuss the theory of two different pseudo-differential operators(p.d.o.)involving Fourier–Jacobi transform associated with a single symbol in.We also derive boundedness results for p.d.o.’s in Sobolev type space.Anewpseudo-differential operator is developed using the product of symbols.Finally,norm inequality for commutators between two pseudo-differential operators is obtained.