A way of constructing translation network operators by Bernstein operators

In the present paper,we provide a way of constructing translation network operators by Bernstein-Durrmeyer operators.     

Boundedness of higher order commutators of generalized fractional integral operators on Hardy spaces

Let Tμ,b,m be the higher order commutator generated by a generalized fractional integral operator Tμ and a BMO function b. In this paper, we will study the boundedness of Tμ,b,m on classical Hardy spaces and Herz-type Hardy spaces.     

A note on multilinear singular integrals with rough kernel

In this paper, the author gives the weighted weak Lipschitz boundedness with power weight for roughmultilinear integral operators. A simple way is obtained that is closely linked with a class of rough frac-tional integral operators.     

Sets which are dense in the space of all Pettis integrable functions

Using the examples given by S.J. Dilworth and M. Girardi, we prove that the set of all nowhere Pettis differentiable functions is a G _δ -dense set in the space of all X-valued Pettis integrable functions on [0, 1]. Also an another example of a dense set in the space of all Pettis integrable functions is given.     

Multivalued linear projections

A multivalued linear projection operator P defined on linear space X is a multivalued linear operator which is idempotent and has invariant domain. We show that a multivalued projection can be characterised in terms of a pair of subspaces and then establish that the class of multivalued linear projections is closed under taking adjoints and closures. We apply the characterisations of the adjoint and completion of a projection together with the closed graph and closed range theorems to give criteria for the continuity of a projection defined on a normed linear space. A new proof of the theorem on closed sums of closed subspaces in a Banach space (cf. Mennicken and Sagraloff [9, 10]) follows as a simple corollary. We then show that the topological decomposition of a space may be expressed in terms of multivalued projections. The paper is concluded with an application to multivalued semi-Fredholm relations with generalised inverses.     

The fractional multilinear singular integral with variable kernels on hardy spaces

The authors discuss Lipschitz boundedness for a class of fractional multilinear operators with variable kernels. It is obtained that these operators are both Lipschitz bounded from Lp to Hq.     

Commutators of BMO functions and singular integral operators with non-smooth kernels on spaces of Homogeneous type of finite measure

Let X be a space of homogeneous type with finite measure. Let T be a singular integral operator which is bounded on Lp (X), 1 ＜ p ＜∞. We give a sufficient condition on the kernel k(x,y) of Tso that when a function b ∈ BMO (X) ,the commutator [b, T] (f) = T (b f) - bT (f) is aounded on spaces Lp for all p, 1 ＜ p ＜∞.     

APPROXIMATION OF A KIND OF NEVAI-DURRMEYER OPERATORS IN Lpw SPACES

The present paper introduces a kind of Nevai-Durrmeyer operators which can be used to approximate functions in Lpw spaces with the weight w(x)=1√1-x2 and the approximate rate is also estimated.     

Proposal of refined interface models and their application for free-edge effect

Two interface models based on physical considerations are proposed to analyze the freeedge effects in unidirectional multilayered composites. The first model is a transition behavior law describing the graded properties of the interlayer between two adjacent layers. It is defined according to the stacking direction and based on a microscopic analysis of the fiber distribution in the vicinity of the interlayer. Used in a numerical simulation, this model gives accurate stress distributions in the laminate, including the interlaminar stresses at the free-edge that are not singular. The second model utilizes an interface law, defined on the material surface, resulting from the asymptotic resolution of an elastic problem pertaining to the interlayer and simulating a very thin flexible layer. This model also gives no singular free-edge interlaminar stresses close to those obtained with the first model.