Continuity of a Class of CalderSn-Zygmund Operators on Certain Besov Spaces

In this paper, we introduce a class of non-convolution-type Calderón-Zygmund operators, whose kernels are certain sums involving the products of the Daubechies wavelets and their convolutions. And we obtain the continuity on the Besov spaces B 0,q p （1 ≤ p, q ≤∞）, which is mainly dependent on the properties of the Daubechies wavelets and Lemari＇s T1 theorem for Besov spaces.     

单位球加权Bergman空间上的Berezin变换与径向算子（英文）

In this paper, we analyze a class of bounded radial operators on the weighted Bergman space A2α(Bn, d Vα), we get that these kinds of operators are diagonal with respect to the standard orthonomal basis. We also investigate the connection between compactness of operators and the boundary behaviour of the corresponding Berezin transform. We further study a special class of radial operators, i.e., Toeplitz operators with a radial L1 symbol.     

Hyponormal Dual Toeplitz Operators on the Orthogonal Complement of the Harmonic Bergman Space

In this paper, we mainly study the hyponormality of dual Toeplitz operators on the orthogonal complement of the harmonic Bergman space. First we show that the dual Toeplitz operator with the bounded symbol is hyponormal if and only if it is normal. Then we obtain a necessary and sufficient condition for the dual Toeplitz operator ■ with the symbol ■ to be hyponormal. Finally, we show that the rank of the commutator of two dual Toeplitz operators must be an even number if the commutator has a fin...     

Biholomorphic Mappings and the Extension Operators on New Hartogs Domains

In this paper, we generalize the Roper–Suffridge operator on the extended Hartogs domains.By using the geometric properties and the growth theorems of subclasses of biholomorphic mappings,we obtain the generalized operators preserve the properties of parabolic and spirallike mappings of type β and order ρ, S*_Ω(β, A, B), almost starlike mapping of complex order λ on ΩN under different conditions, and thus we get the corresponding results on the unit ball B~n in C~n. The conclusions lead to some known results.     

Continuity properties for commutators of multilinear type operators on product of certain Hardy spaces

Similar to the property of a linear Calderdn-Zygmund operator, a linear fractional type operator Is associated with a BMO function b fails to satisfy the continuity from the Hardy space Hp into Lp for p ≤ 1. Thus, an alternative result was given by Y. Ding, S. Lu and P. Zhang, they proved that [b,Iα] is continuous from an atomic Hardy space Hp b into Lp, where Hp b is a subspace of the Hardy space Hp for n/（n ＋ 1） 〈 p ≤ 1. In this paper, we study the commutators of multilinear fractional type operators on product of certain Hardy spaces. The endpoint （Hp1 b1 ×... × HP2, Lp） boundedness for multilinear fractional type operators is obtained. We also give the boundedness for the commutators of multilinear Calderdn-Zygmund operators and multilinear fractional type operators on product of certain Hardy spaces when b ∈ （Lipβ）m（Rn）.     

Wey1代数中的消元法及恒等式（英）

In paper [1], Zeilberger presented an approach to special functions identities, besides providing a general mathematical framework for the proof machinery, which leads to mathematically and algorithmically challenging questions such as elimination in noncommutatire operator algebras (Weyl algebra). By the impetus of this approach, we study the elimination under the shift operators.     

Schatten-p Class(0<p≤∞) Toeplitz Operators on Generalized Fock Spaces

In this paper, we discuss the Schatten-p class(0 p ≤∞) of Toeplitz operators on generalized Fock space with the symbol in positive Borel measure. It makes a great difference from other papers by using the estimates of the kernel and the weight together instead of separately estimating each other. We also get the equivalent conditions when a Toeplitz operator is in the Schatten-p class.     

CAUCHY TYPE INTEGRALS AND A BOUNDARY VALUE PROBLEM IN A COMPLEX CLIFFORD ANALYSIS

Clifford analysis is an important branch of modern analysis;it has a very important theoretical significance and application value,and its conclusions can be applied to the Maxwell equation,Yang-Mill field theory,quantum mechanics and value problems.In this paper,we first give the definition of a quasi-Cauchy type integral in complex Clifford analysis,and get the Plemelj formula for it.Second,we discuss the H?lder continuity for the Cauchy-type integral operators with values in a complex Cliffor...     

Toeplitz算子在Dirichlet空间上的亚正规性

In this paper,we prove that the necessary and sufficient condition for a Toeplitz operator Tu on the Dirichlet space to be hyponormal is that the symbol u is constant for the case that the projection of u in the Dirichlet space is a polynomial and for the case that u is a class of special symbols,respectively.We also prove that a Toeplitz operator with harmonic polynomial symbol on the harmonic Dirichlet space is hyponormal if and only if its symbol is constant.     

Norm estimates of w-circulant operator matrices and isomorphic operators for w-circulant algebra

An n × n ω-circulant matrix which has a specific structure is a type of important matrix. Several norm equalities and inequalities are proved for ω-circulant operator matrices with ω = e~(iθ)(0≤θ 2π) in this paper. We give the special cases for norm equalities and inequalities, such as the usual operator norm and the Schatten p-norms. Pinching type inequality is also proposed for weakly unitarily invariant norms. Meanwhile,we present that the set of ω-circulant matrices with complex entries has an idempotent basis. Based on this basis, we introduce an automorphism on the ω-circulant algebra and then show different operators on linear vector space that are isomorphic to the ω-circulant algebra. The function properties, other idempotent bases and a linear involution are discussed for ω-circulant algebra. These results are closely related to the special structure of ω-circulant matrices.     

Context-free grammars for triangular arrays

We consider context-free grammars of the form G = {f → fb1+b2+1ga1+a2, g → fb1 ga1+1},where ai and bi are integers sub ject to certain positivity conditions. Such a grammar G gives rise to triangular arrays {T(n, k)}0≤k≤n satisfying a three-term recurrence relation. Many combinatorial sequences can be generated in this way. Let Tn (x) =∑nk=0T(n, k)xk. Based on the differential operator with respect to G, we define a sequence of linear operators Pn such that Tn+1(x) = Pn(Tn(x)). Applying the characterization of real stability preserving linear operators on the multivariate polynomials due to Borcea and Br?ndén, we obtain a necessary and sufficient condition for the operator Pn to be real stability preserving for any n. As a consequence, we are led to a sufficient condition for the real-rootedness of the polynomials defined by certain triangular arrays, obtained by Wang and Yeh.Moreover, as special cases we obtain grammars that lead to identities involving the Whitney numbers and the Bessel numbers.     

Little Hankel Operators on the Weighted Bergman Space of the Unit Ball

In this paper we mainly consider little Hankel operators with squareintegrable symbols on the weighted Bergman spaces of the unit ball.We obtain that Schatten class of little Hankel operators is equivalent to Schatten class of positive Toeplitz operators under the conditions that SMO（f） ∈ L p/2 （B n,dλ） and 2 ≤ p ∞,which is very important to research the relation between Toeplitz operators and little Hankel operators.     

Weighted estimates for multilinear pseudodifferential operators

In this paper,we study the weighted estimates for multilinear pseudodifferential operators.We show that a multilinear pseudodifferential operator is bounded with respect to multiple weights whenever its symbol satisfies some smoothness and decay conditions.Our result generalizes similar ones from the classical Ap weights to multiple weights.     

TWO-DIMENSIONAL MAXIMAL OPERATOR OF DYADIC DERIVATIVE ON VILENKIN MARTINGALE SPACES

In [1] the boundedness of one dimensional maximal operator of dyadic derivative is discussed.In this paper,we consider the two-dimensional maximal operator of dyadic derivative on Vilenkin martingale spaces.With the help of counter-example we prove that the maximal operator is not bounded from the Hardy space H q to the Hardy space H q for 0相似文献   

Local Solvability and Propagation of Singularities for a Class of Psendodifferential Operators with Irregular Singularity

Consider a class of pseudodifferential operators which satisfy the conditions 1—4 (or 4').By microlocal analysis, we can reduce the operators to $\[P = {t^m}\frac{\partial }{{\partial t}} - B(x,t,{D_x},{D_t})\]$ ($\[B \in L_C^0,m > 1\]$ is integer), which we call non-Fuchsian operators. Then, we give an explicit construction for the microlocal right and left parametrices of these operators near multi-characteristics and compute wave front sets of those parametrices. Finally, we study the local solvability and the propagation of singularities for the equation corresponding to the non-Fuchsian operator. In order to obtain the previous results, the following are noteworthy. 1 The singularity of the operators $\[{t^m}\frac{\partial }{{\partial t}} - B\]$ is concentrated on $\[{t^m}\frac{\partial }{{\partial t}}\]$, So,for simplicity, we may suppose that B depends only on x and D_x. Obviously, it will lead to considerable simplification of working process. 2 It's necessary to distinguish the odd integer m from even, however, we can study these different cases in the same way. In this paper, we study only that m is odd; i. e. $\[P = {t^{2N + 1}}\frac{\partial }{{\partial t}} - 2NB(x,{D_x})\]$ (N>=1 integer) (2) 3 We have to make some hypothesis about B to obtain local solvability. Here we assume $\[{\mathop{\rm Re}\nolimits} ({b_0}(x,\xi )) < 0\]$ near characteristic point, (3) where $\[{b_0}(x,\xi )\]$ is the principal symbol of B(x, D_x). By the discussion on this subject we prove that the operator (2) is, under the assumption (3), $\[{C^\infty } - locally\]$ solvable near the multi-characteristic point (x_0, 0); and obtain the following result for the propagation of singularities: Assume the multi- oharacteristio point (x_0,0,\xi_0,0) of the operator (2) doesn't belong to WF(pu). Let v denote the null bicharaoteristio strip of symbol to through (x_0, 0,\xi_0,0). Then, if $\[WF(u) \cap v\backslash \{ ({x_0},0,{\xi _0},0)\} = \phi \]$, we have $\[({x_0},0,{\xi _0},0) \notin WF(u)\]$.     

PROPERTIES OF THE MODIFIED ROPER-SUFFRIDGE EXTENSION OPERATORS ON REINHARDT DOMAINS

In this paper,we mainly discuss the properties of the modified Roper-Suffridge operators on Reinhardt domains.By the analytical characteristics and distortion results of subclasses of biholomorphic mappings,we conclude that the modified Roper-Suffridge operators preserve the properties of S_Ω~*(β,A,B),almost starlike mapping of complex orderλ on Ω_(n,p2,…,pn).Sequentially,we get that the modified Roper-Suffridge operators preserve spirallikeness of type β and order a,strongly pirallikeness of type β and order α,almost starlikeness of order α on Ω_(n,p2,…,pn).The conclusions provide a new approach to construct these biholomorphic mappings which have special geometric properties in several complex variables.     

Complex geometry and real geometry

There is a well-known way to generalize the Riemann-Roch operator for Kahler manifold to that for Hermitian manifold. In this paper we show a slightly different way to get a generalized Riemann-Roch operator, which is just the Dirac operator. The difference between the two operators is that the latter one enables the so-called Pythagoras equalities.     

Hausdorff operators on the Heisenberg group

This paper is devoted to the high-dimensional and multilinear Hausdorff operators on the Heisenberg group H n. The sharp bounds for the strong type(p, p)(1 ≤ p ≤∞) estimates of n-dimensional Hausdorff operators on H n are obtained. The sharp bounds for strong(p, p) estimates are further extended to multilinear cases. As an application, we derive the sharp constant for the multilinear Hardy operator on H n. The weak type(p, p)(1 ≤ p ≤∞) estimates are also obtained.     

SZEG KERNEL FOR HARDY SPACE OF MATRIX FUNCTIONS

By the characterization of the matrix Hilbert transform in the Hermitian Clifford analysis, we introduce the matrix Szeg¨o projection operator for the Hardy space of Hermitean monogenic functions defined on a bounded sub-domain of even dimensional Euclidean space,establish the Kerzman-Stein formula which closely connects the matrix Szeg projection operator with the Hardy projection operator onto the Hardy space, and get the matrix Szeg projection operator in terms of the Hardy projection operator and its adjoint. Furthermore,we construct the explicit matrix Szeg¨o kernel function for the Hardy space on the sphere as an example, and get the solution to a boundary value problem for matrix functions.     

RIESZ IDEMPOTENT AND BROWDER＇S THEOREM FOR ABSOLUTE-（p,r ）-PARANORMAL OPERATORS

An operator T is said to be paranormal if ||T 2x|| ≥ ||T x||2 holds for every unit vector x.Several extensions of paranormal operators are considered until now,for example absolute-k-paranormal and p-paranormal introduced in [10],[14],respectively.Yamazaki and Yanagida [38] introduced the class of absolute-(p,r)-paranormal operators as a further generalization of the classes of both absolute-k-paranormal and p-paranormal operators.An operator T ∈ B(H) is called absolute-(p,r)-paranormal operator if |||T |p|T |r x||r ≥ |||T |rx||p+r for every unit vector x ∈ H and for positive real numbers p > 0 and r > 0.The famous result of Browder,that self adjoint operators satisfy Browder’s theorem,is extended to several classes of operators.In this paper we show that for any absolute-(p,r)paranormal operator T,T satisfies Browder’s theorem and a-Browder’s theorem.It is also shown that if E is the Riesz idempotent for a nonzero isolated point μ of the spectrum of a absolute-(p,r)-paranormal operator T,then E is self-adjoint if and only if the null space of T μ,N(T μ) N(T μ).