the object of this paper is to establish certain generalized fractional integration and differentiation involving generalized mittag-leffler function defined by salim and faraj [25]. the considered generalized fractional calculus operators contain the appell's function $f_3$ [2, p.224] as kernel and are introduced by saigo and maeda [23]. the marichev-saigo-maeda fractional calculus operat...

We characterize compact composition operators on real Banach spaces of complex-valued bounded Lipschitz functions on metric spaces, not necessarily compact, with Lipschitz involutions and determine their spectra.

in this paper we obtain lower and upper estimates for the essential norms of generalized composition operators from weighted dirichlet spaces or bloch type spaces to $q_k$ type spaces.

‎In this paper‎, ‎we study weighted composition operators between Lipschitz algebras of complex-valued bounded functions on metric spaces‎, ‎not necessarily compact‎. ‎We give necessary and sufficient conditions for the injectivity and the surjectivity of these operators‎. ‎We also obtain sufficient and necessary conditions for a weighted composition operator between these spaces to be compact.

In this paper, we study two types of the reducing subspaces for the weighted composition operator $W: frightarrow ucdot fcirc varphi$ on $L^2(Sigma)$. A necessary and sufficient condition is given for $W$ to possess the reducing subspaces of the form $L^2(Sigma_B)$ where $Bin Sigma_{sigma(u)}$. Moreover, we pose some necessary and some sufficient conditions under which the subspaces of the form...

In [1] D. Harrington and R. Whitley examined several questions of seminormality for composition operators. In that article they raise the question of finding a measure theoretic characterization of hyponormality for composition operators. In this article we establish criteria for hyponormality for weighted composition operators. By restricting attention to the case of weight function equal to 1...

A composition operator Tbf = f o b is completely continuous on H1 if and only if \b\ < 1 a.e. If the adjoint operator Tg is completely continuous on VMOA , then 7¿ is completely continuous on Hl . Examples are given to show that the converse fails in general. Two results are given concerning the relationship between the complete continuity of an operator and of its adjoint in the presence of ce...