SOME PROPERTIES OF THE INTEGRATION OPERATORS ON THE SPACES F(p,q,s)

We study the closed range property and the strict singularity of integration operators acting on the spaces F(p,pα-2,s).We completely characterize the closed range property of the Volterra companion operator I_g on F(p,pα-2,s),which generalizes the existing results and answers a question raised in [A.Anderson,Integral Equations Operator Theory,69(2011),no.1,87-99].For the Volterra operator J_g,we show that,for 0 <α≤1,J_g never has a closed range on F(p,pα-2,s).We...     

Closed Range Composition Operators on a General Family of Function Spaces

In this paper, necessary and sufficient conditions for a closed range composition operator C_φ on the general family of holomorphic function spaces F( p, q, s) and more generally on α-Besov type spaces F( p, αp-2, s) are given. We give a Carleson measure characterization on F( p, α p-2, s) spaces, then we indicate how Carleson measures can be used to characterize boundedness and compactness of C_φ on F( p, q, s) and F( p, αp-2, s) spaces.     

Boundedness of parabolic singular integrals and Marcinkiewicz integrals on Triebel-Lizorkin spaces

In this paper,we obtain the boundedness of the parabolic singular integral operator T with kernel in L(logL)1/γ(Sn-1) on Triebel-Lizorkin spaces.Moreover,we prove the boundedness of a class of Marcinkiewicz integrals μΩ,q(f) from ∥f∥ F˙p0,q(Rn) into Lp(Rn).     

L~p CONTINUITY OF HRMANDER SYMBOL OPERATORS OpS_（0,0） ~m AND NUMERICAL ALGORITHM

If we use Littlewood-Paley decomposition, there is no pseudo-orthogonality for Ho¨rmander symbol operators OpS m 0 , 0 , which is different to the case S m ρ,δ (0 ≤δ < ρ≤ 1). In this paper, we use a special numerical algorithm based on wavelets to study the L p continuity of non infinite smooth operators OpS m 0 , 0 ; in fact, we apply first special wavelets to symbol to get special basic operators, then we regroup all the special basic operators at given scale and prove that such scale operator’s continuity decreases very fast, we sum such scale operators and a symbol operator can be approached by very good compact operators. By correlation of basic operators, we get very exact pseudo-orthogonality and also L 2 → L 2 continuity for scale operators. By considering the influence region of scale operator, we get H 1 (= F 0 , 2 1 ) → L 1 continuity and L ∞→ BMO continuity. By interpolation theorem, we get also L p (= F 0 , 2 p ) → L p continuity for 1 < p < ∞ . Our results are sharp for F 0 , 2 p → L p continuity when 1 ≤ p ≤ 2, that is to say, we find out the exact order of derivations for which the symbols can ensure the resulting operators to be bounded on these spaces.     

THE SINE TRANSFORM OPERATOR IN THE BANACH SPACE OF SYMMETRIC MATRICES AND ITS APPLICATION IN IMAGE RESTORATION

In this paper, we study an operator s which maps every n-by-n symmetric matrix A, to a matrix s(A_n) that minimizes || B_n-A_n || F over the set of all matrices B_n, that can be diagonalized by the sine transform. The matrix s(A_n), called the optimal sine transform preconditioner, is defined for any n-by-n symmetric matrices A_n. The cost of constructing s(A_n) is the same as that of optimal circulant preconditioner c(A_n) which is defined in [8], The s(A_n) has been proved in [6] to be a good preconditioner in solving symmetric Toeplitz systems with the preconditioned conjugate gradient (PCG) method. In this paper, we discuss the algebraic and geometric properties of the operator s, and compute its operator norms in Banach spaces of symmetric matrices. Some numerical tests and an application in image restoration are also given.     

μ-AVERAGE N-WIDTHS ON THE WIENER SPACE

In this paper we investigate the asymptotic bebaviour of μ-average n-widths of integral operator Kon the Wiener space. where K is the inverse operator of an ordinary linear differential operator L of orderm. For 1≤p.q<∞ C_n~a(K,W)_(p,q)a_n~a(K,W)_(p,q)n~(-(m)-(1/2)and for p∈(1,∞), q∈(2,∞) d_n~a(K; W)_(p.q)n~(-(m)-(1/2)).     

Infinitely Many Solutions for Schr?dinger–Choquard–Kirchhoff Equations Involving the Fractional p-Laplacian

In this article,we show the existence of infinitely many solutions for the fractional pLaplacian equations of Schr?dinger-Kirchhoff type equation ■ ,where(-△)_p~s is the fractional p-Laplacian operator,[u]_(s,p) is the Gagliardo p-seminorm,0 s 1 q p N/s,α∈(0,N),M and V are continuous and positive functions,and k(x) is a non-negative function in an appropriate Lebesgue space.Combining the concentration-compactness principle in fractional Sobolev space and Kajikiya's new version of the symmetric mountain pass lemma,we obtain the existence of infinitely many solutions which tend to zero for suitable positive parameters λ and β.     

On F(p,s)-Teichmüller Space

In this paper, we determine the differential of the Bers projection at the origin in the F(p, s)-Teichmüller space.     

消失的弱~Morrey 型空间上某些算子的刻画

In this paper we mainly give some characterizations for the boundedness of the weight Hardy operator, maximal operator, potential operator and singular integral operator on the vanishing generalized weak Morrey spaces V W L_Π~(p,φ)(?) with bounded set ?.     

Fixed Point Theory for 1-Set Weakly Contractive Operators in Banach Spaces

In this work, using an analogue of Sadovskii＇s fixed point result and several important inequalities we investigate and give new existence theorems for the nonlinear operator equation F（x） =μx, （μ≥1） for some weakly sequentially continuous, weakly condensing and weakly 1-set weakly contractive operators with different boundary conditions. Correspondingly, we can obtain some applicable fixed point theorems of Leray-Schauder, Altman and Furi-Pera types in the weak topology setting which generalize and improve the corresponding results of [3,15,16].     

The ρ-variation of the Hermitian Riesz transform

In this paper we prove the behaviour in weighted Lp spaces of the oscillation and variation of the Hilbert transform and the Riesz transform associated with the Hermite operator of dimension 1. We prove that this operator maps LP（R, w（x）dx） into itself when w is a weight in the Ap class for 1 〈 p 〈 ∞. For p = 1 we get weak type for the A1 class. Weighted estimated are also obtained in the extreme case p = ∞.     

STARLIKENESS AND SUBORDINATION PROPERTIES OF A LINEAR OPERATOR

In this paper, we introduce a new class of p-valent analytic functions defined by using a linear operator Lαk. For functions in this class Hαk(p, λ; h) we estimate the coefficients.Furthermore, some subordination properties related to the operator Lαkare also derived.     

The Brezis–Nirenberg Problem for the Fractional p-Laplacian in Unbounded Domains

In this paper we study the existence of nontrivial solutions to the well-known Brezis–Nirenberg problem involving the fractional p-Laplace operator in unbounded cylinder type domains.By means of the fractional Poincaré inequality in unbounded cylindrical domains, we first study the asymptotic property of the first eigenvalue λp,s(■) with respect to the domain■. Then, by applying the concentration-compactness principle for fractional Sobolev spaces in unbounded domains, we prove the existence res...     

性质$(\omega)$的注解

In this note we study the property （ω）, a variant of Weyl＇s theorem introduced by Rakocevic, by means of the new spectrum. We establish for a bounded linear operator defined on a Banach space a necessary and sufficient condition for which both property （ω） and approximate Weyl＇s theorem hold. As a consequence of the main result, we study the property （ω） and approximate Weyl＇s theorem for a class of operators which we call the λ-weak-H（p） operators.     

SOME NONLINEAR OPERATOR EQUATIONS AND THEIR APPROXIMATE SOLUTIONS

Consider nonlinear operator equation: Ax Fx=α, where A is a dense closed linear operator, F is a nonlinear operator. In this paper, we shall give the criterion about solution existence of this equation and the convergence criterion of Galerkin approximate solutions.     

Boundedness of a class of super singular integral operators and the associated commutators

In this paper we give the (Lα p, Lp) boundedness of the maximal operator of a class of super singular integrals defined bywhich improves and extends the known result. Moreover, by applying an off-Diagonal T1 Theorem, we also obtain the (Lp, Lq) boundedness of the commutator defined by     

SOME NONLINEAR OPERATOR EQUATIONS AND THEIR APPROXIMATE SOLUTIONS

Consider nonlinear operator equation, Ax+Fx=α, where A is a dense closed linear operator, F is a nonlinear operator. In this paper, we shall give the criterion about solution existence of this equation and the convergence criterion of Galerkln approximate solutions.     

Certain averaging operators on Triebel-Lizorkin spaces

Abstract. In this article, we study the boundedness properties of the averaging operator S_t^γon Triebel-Lizorkin spaces■ for various p, q. As an application, we obtain the norm convergence rate for S_t^γ(f ) on Triebel-Lizorkin spaces and the relation between the smoothness imposed on functions and the rate of norm convergence of S_t^γis given.     

$R^n$空间中的Cauchy积分公式

In this note p(D) = Dm+ b1Dm 1+···+ bmis a polynomial Dirac operator in R~n, where D =nj=1ej xjis a standard Dirac operator in Rn, bjare the complex constant coefficients. In this note we discuss all decompositions of p(D) according to its coefficients bj,and obtain the corresponding explicit Cauchy integral formulae of f which are the solution of p(D)f = 0.     

Boundedness of Hausdorff operators on Lebesgue spaces and Hardy spaces

In this paper, we study the boundedness of the Hausdorff operator H_? on the real line R. First, we start with an easy case by establishing the boundedness of the Hausdorff operator on the Lebesgue space L~p(R)and the Hardy space H~1(R). The key idea is to reformulate H_? as a Calder′on-Zygmund convolution operator,from which its boundedness is proved by verifying the Hrmander condition of the convolution kernel. Secondly,to prove the boundedness on the Hardy space H~p(R) with 0 p 1, we rewrite the Hausdorff operator as a singular integral operator with the non-convolution kernel. This novel reformulation, in combination with the Taibleson-Weiss molecular characterization of H~p(R) spaces, enables us to obtain the desired results. Those results significantly extend the known boundedness of the Hausdorff operator on H~1(R).