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.     

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.     

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.     

Boundedness of multilinear operators on weighted herz type spaces

In this paper, the author establishes the boundedness of multilinear operators on weighted Herz spaces and Herz-type Hardy spaces. The author also obtains their weak estimates on endpoints. As a special case, the conclusions may lead to the weighted estimates for multilinear Calderon-Zygmund operators.     

On strong approximation applied to post-widder operators

We introduce modified Post-Widder operators in polynomial weighted spaces of differentiable functions and we study strong approximation for them.     

An application of Bernstein-Durrmeyer operators

In the present paper, we find that the Bemstein-Durrmeyer operators, besides their better applications in approximation theory and some other fields, are good tools in constructing translation network. With the help of the de la Vallee properties of the Bernstein-Durrmeyer operators a sequence of translation network operators is constructed and its degree of approximation is dealt.     

Weighted estimate for the multilinear oscillatory singular integral operators

In this paper, the weighted L^p(R^n) boundedness for the multilinear oscillatory singular integral operators with polynomial phases is studied.     

WEIGHTED L^p-APPROXIMATION BY THE MODIFIED NEVAI OPERATORS

The present paper gives a Jackson type estimate for Nevai operators under weighted Lp norm, and establishes the direct and converse theorems in some proper Besov spaces.