PRODUCT TYPE OPERATORS ACTING BETWEEN WEIGHTED BERGMAN SPACES AND BLOCH TYPE SPACES

For analytic functions u,ψin the unit disk D in the complex plane and an analytic self-mapφof D,we describe in this paper the boundedness and compactness of product type operators T_(u,ψ,φ)f(z)=u(z)f(φ(z))+ψ(z)f'(φ(z)),z∈D,acting between weighted Bergman spaces induced by a doubling weight and a Bloch type space with a radial weight.

TOEPLITZ OPERATORS BETWEEN WEIGHTED BERGMAN SPACES OVER THE HALF-PLANE

In this paper,by characterizing Carleson measures,we investigate a class of bounded Toeplitz operator between weighted Bergman spaces with Békolléweights over the half-plane for all index choices.

两类加权空间间的积分算子与离散算子的有界性及算子范数估计

Using the weight coefficient method, we first discuss semi-discrete Hilbert-type inequalities, and then discuss boundedness of integral and discrete operators and operator norm estimates based on Hilbert-type inequalities in weighted Lebesgue space and weighted normed sequence space.

THE BOUNDEDNESS OF OPERATORS ON WEIGHTED MULTI-PARAMETER LOCAL HARDY SPACES

Though atomic decomposition is a very useful tool for studying the boundedness on Hardy spaces for some sublinear operators,untill now,the boundedness of operators on weighted Hardy spaces in a multi-parameter setting has been established only by almost orthogonality estimates.In this paper,we mainly establish the boundedness on weighted multi-parameter local Hardy spaces via atomic decomposition.

The Interpolation of Operators between Weighted Hardy Spaces and Weighted L^p Spaces

The paper is given the interpolation of operators between weighted Hardy spaces and weighted L p spaces when w∈A 1 by Calderon Zygmund decomposition.

Weighted boundedness of some integral operators on weighted λ-central Morrey space

In this paper, the authors prove the weighted boundedness of singular integral and fractional integral with a rough kernel on the weighted λ-central Morrey space. Moreover, the weighted estimate for commutators of singular integral with a rough kernel on the weighted λ-central Morrey space is also given.

ANOTHER CHARACTERIZATIONS OF MUCKENHOUPT A_p CLASS

This manuscript addresses Muckenhoupt Ap weight theory in connection to Mor- rey and BMO spaces. It is proved that a; belongs to Muckenhoupt Ap class, if and only if Hardy-Littlewood maximal function M is bounded from weighted Lebesgue spaces LP（w） to weighted Morrey spaces Mpq（ω） for 1 〈 q 〈 p 〈 ∞. As a corollary, if M is （weak） bounded on Mpq（ω）, then ω∈Ap. The Ap condition also characterizes the boundedness of the Riesz transform Rj and convolution operators Tε on weighted Morrey spaces. Finally, we show that ω∈Ap if and only if ω∈BMOp＇ （ω） for 1 ≤ p 〈 ∞ and 1/p ＋ 1/p＇ = 1.

The Boundedness of Littlewood-Paley Operators with Rough Kernels on Weighted (L^q , L^p )~α (R^n) Spaces

In this paper, we shall deal with the boundedness of the Littlewood-Paley operators with rough kernel. We prove the boundedness of the Lusin-area integral μΩs and Littlewood-Paley functions μΩ and μλ^＊ on the weighted amalgam spaces （Lω^q,L^p）^α（R^n）as 1〈q≤α〈p≤∞.

WEIGHTED COMPOSITION OPERATORS ON WEIGHTED DIRICHLET SPACES

We characterize the boundedness and compactness of weighted composition operators on weighted Dirichlet spaces in terms of Nevanlinna counting functions and Caxleson measure.

THE EXISTENCE OF A NONTRIVIAL WEAK SOLUTION TO A DOUBLE CRITICAL PROBLEM INVOLVING A FRACTIONAL LAPLACIAN IN R^N WITH A HARDY TERM

In this paper,we consider the existence of nontrivial weak solutions to a double critical problem involving a fractional Laplacian with a Hardy term:(−Δ)s u−γu|x|2s=|u|2∗s(β)−2 u|x|β+[Iμ∗Fα(⋅,u)](x)fα(x,u),u∈H˙s(R n),(0.1)(1)where s∈(0,1),0≤α,β<2s<n,μ∈(0,n),γ<γH,Iμ(x)=|x|−μ,Fα(x,u)=|u(x)|2#μ(α)|x|δμ(α),fα(x,u)=|u(x)|2#μ(α)−2 u(x)|x|δμ(α),2#μ(α)=(1−μ2n)⋅2∗s(α),δμ(α)=(1−μ2n)α,2∗s(α)=2(n−α)n−2s andγH=4 sΓ2(n+2s4)Γ2(n−2s4).We show that problem(0.1)admits at least a weak solution under some conditions.To prove the main result,we develop some useful tools based on a weighted Morrey space.To be precise,we discover the embeddings H˙s(R n)↪L 2∗s(α)(R n,|y|−α)↪L p,n−2s2 p+pr(R n,|y|−pr),(0.2)(2)where s∈(0,1),0<α<2s<n,p∈[1,2∗s(α))and r=α2∗s(α).We also establish an improved Sobolev inequality,(∫R n|u(y)|2∗s(α)|y|αdy)12∗s(α)≤C||u||θH˙s(R n)||u||1−θL p,n−2s2 p+pr(R n,|y|−pr),∀u∈H˙s(R n),(0.3)(3)where s∈(0,1),0<α<2s<n,p∈[1,2∗s(α)),r=α2∗s(α),0<max{22∗s(α),2∗s−12∗s(α)}<θ<1,2∗s=2nn−2s and C=C(n,s,α)>0 is a constant.Inequality(0.3)is a more general form of Theorem 1 in Palatucci,Pisante[1].By using the mountain pass lemma along with(0.2)and(0.3),we obtain a nontrivial weak solution to problem(0.1)in a direct way.It is worth pointing out that(0.2)and 0.3)could be applied to simplify the proof of the existence results in[2]and[3].

ON F(p,q,s)SPACES

The family of spaces F(p,q,s)was introduced by the author in 1996.Since then,there has been great development in the theory of these spaces,due to the fact that these spaces include many classical function spaces,and have connections with many other areas of mathematics.In this survey we present some basic properties and recent results on F(p,q,s)spaces.

Some Estimates for Commutators of Fractional Integrals Associated to Operators with Gaussian Kernel Bounds on Weighted Morrey Spaces

Let L be the infinitesimal generator of an analytic semigroup on L^2 （R^n） with Gaussian kernel bound, and let L^-α/2 be the fractional integrals of L for 0 〈 α 〈 n. In this paper, we will obtain some boundedness properties of commutators [b, L^-α/2] on weighted Morrey spaces L^p,k（w） when the symbol b belongs to BMO（Rn） or the homogeneous Lipschitz space.

MULTIPLIERS AND RELATIVE COMPLETION IN WEIGHTED LORENTZ SPACES

Let G be a locally compact Abelian group with Haar measure μ. In the present paper, first the authors discussed some properties of weighted Lorentz space. Then they defined the relative completion A of a subspace A of the weighted Lorentz space, and showed that the space of the multipliers from L_w~1,(G) to A is algebrically isomorphic and homeomorphic to A.

APPROXIMATION OF A KIND OF NEVAI-DURRMEYER OPERATORS IN L_w^p SPACES

The present paper introduces a kind of Nevai-Durrmeyer operators which can be used to approximate functions in Lω^p, spaces with the weight ω（x）=1/√（1-x^2） and the approximate rate is also estimated.

Weak Type Estimates for Intrinsic Square Functions on Weighted Morrey Spaces

In this paper, we will obtain the weak type estimates of intrinsic square func- tions including the Lusin area integral, Littlewood-Paley g-function and g^-function on the weighted Morrey spaces L^1,k （w） for 0〈k〈 1 and w ∈ A1.

ATTRACTORS FOR THE GINZBURG-LANDAU-BBM EQUATIONS IN AN UNBOUNDED DOMAIN

By the interpolating inequality and a priori estimates in the weighted space,the existence of the global solutions for the Ginzburg-Landau equation coupled with the BBM equation in an unbounded domain is considered, and the existence of the maximal attractor is obtained.

ON COMPACTNESS FOR ITERATED COMMUTATORS

The authors study the iterated commutators on the weighted Bergman spaces A2（φ）, and prove that Cnh is compact on A2（φ） if and only if h ∈ B0.

THE WEIGHTED HERZ-TYPE HARDY SPACES hK_q^(α,p)(ω_1,ω_2)

Let (.the Muckenhoupt class). In this paper, the author introduce the weighted Herz-type Hardy spaces (w2) and present their atomic decomposition. Using the atomic decomposition, the author find out their dual spaces, establish the boundedness on these spaces of the pseudo-differential operators of order zero and show that , the class of C(Rn)-functions with compactly support, is dense in and there is a subsequence, which converges in distrbutional sense to some distribution of , of any bounded sequence in In addition, the author also set up the boundedness of some non-linear quantities in compensated compactness.

MULTIPLIERS AND TENSOR PRODUCTS OF WEIGHTED L^p-SPACES

Let G be a locally compact unimodular group with Haar measure rmdx and ω be the Beurling's weight function on G (Reiter, [10]). In this paper the authors define a space Aωp,q (G) and prove that Aωp,q (G) is a translation invariant Banach space. Fur- thermore the authors discuss inclusion properties and show that if G is a locally compact abelian group then Aωp,q (G) admits an approximate identity bounded in Lω1 (G). It is also proved that the space Lωp (G) Lω1 Lωq (G) is isometrically isomorphic to the space Aωp,q (G) and the space of multipliers from Lωp (G) to Lq-1, (G) is isometrically isomorphic to the dual of the space Aωp,q (G) iff G satisfies a property Ppq. At the end of this work it is showed that if G is a locally compact abelian group then the space of all multipliers from Lω1 (G) to Aωp,q (G) is the space Aωp,q (G).

Using Genetic Algorithms to Improve the Search of the Weight Space in Cascade－Correlation Neural Network

In this paper, we use the global search characteristics of genetic algorithms to help search the weight space of the neurons in the cascade-correlation architecture. The cascade-correlation learning architecture is a technique of training and building neural networks that starts with a simple network of neurons and adds additional neurons as they are needed to suit a particular problem. In our approach, instead ofmodifying the genetic algorithm to account for convergence problems, we search the weight-space using the genetic algorithm and then apply the gradient technique of Quickprop to optimize the weights. This hybrid algorithm which is a combination of genetic algorithms and cascade-correlation is applied to the two spirals problem. We also use our algorithm in the prediction of the cyclic oxidation resistance of Ni- and Co-base superalloys.