The continuity for some multilinear operators related to certain fractional singular integral operators on Triebel-Lizorkin spaces is obtained. The operators include Calderon-Zygmund singular integral operator and fractional integral operator. 1. Introduction. Let T be a Calderon-Zygmund singular integral operator; a well-known result of Coifman et al. (see [6]) states that the commutator [b, T...

In this paper, we introduce a new general integral operator and obtain the order of convexity of this integral operator.

In [4], Breaz and Breaz gave the univalence conditions of the integral operator Fα,n of the analytic functions belonging to the classes T2, T2,μ and S(p). The purpose of this paper is to generalize the integral operator Fα,n by means of the generalized Al-Oboudi differential operator and investigate univalence conditions of this generalized integral operator considering the classes Tj , Tj,μ an...

We prove a local T (b) theorem for singular integral operators in the spirit of the one for perfect dyadic singular integral operators obtained by Hofmann, Muscalu, Thiele, Tao and the first author. The method consists in reducing one situation to the other by representing via the Beylkin-Coifman-Rokhlin algorithm any singular integral operator with truncated kernel as the sum of a bounded oper...

In this paper, we consider a particular class of integral equations of the fourth kind and show that tractability and differentiability index of the given system are 3. Tractability and dierentiability index are introduced based on the-smoothing property of a Volterra integral operator and index reduction procedure, respectively. Using the notion of index, we give sucient conditions for the exi...