GENERALIZED FORELLI-RUDIN TYPE OPERATORS BETWEEN SEVERAL FUNCTION SPACES ON THE UNIT BALL OF C^(N)

In this paper,we investigate sufficient and necessary conditions such that generalized Forelli-Rudin type operators T_(λ,τ,k),S_(λ,τ,k),Q_(λ,τ,k)and R_(λ,τ,k)are bounded between Lebesgue type spaces.In order to prove the main results,we first give some bidirectional estimates for several typical integrals.

Solving Neumann Boundary Problem with Kernel-Regularized Learning Approach

We provide a kernel-regularized method to give theory solutions for Neumann boundary value problem on the unit ball. We define the reproducing kernel Hilbert space with the spherical harmonics associated with an inner product defined on both the unit ball and the unit sphere, construct the kernel-regularized learning algorithm from the view of semi-supervised learning and bound the upper bounds for the learning rates. The theory analysis shows that the learning algorithm has better uniform convergence according to the number of samples. The research can be regarded as an application of kernel-regularized semi-supervised learning.

AN INTEGRAL ESTIMATE AND THE EQUIVALENT NORMS ON F(p, q, s, k) SPACES IN THE UNIT BALL

In this article, the authors give a typical integral＇s bidirectional estimates for allcases. At the same time, several equivalent characterizations on the F（p, q, s, k） space in theunit ball of Cn are given.

UNIFORMLY STARLIKE MAPPINGS AND UNIFORMLY CONVEX MAPPINGS ON THE UNIT BALL B^n

In this article, we extend the definition of uniformly starlike functions and uni- formly convex functions on the unit disk to the unit ball in C^n, give the discriminant criterions for them, and get some inequalities for them.

SCHWARZ-PICK ESTIMATES FOR PARTIAL DERIVATIVES OF ARBITARY ORDER OF BOUNDED HOLOMORPHIC FUNCTIONS IN THE UNIT BALL OF C^n

This paper gives a Schwarz-Pick estimate for bounded holomorphic functions in the unit ball of C n .

Weighted composition operators from F(p,q,s) spaces to Bers-type spaces in the unit ball

This paper deals with the boundedness and compactness of the weighted composition operators from the F（p, q, s） spaces, including Hardy space, Bergman space, Qp space, BMOA space, Besov space and α-Bloch space, to Bers-type spaces Hv^∞（ or little Bers-type spaces Hv,o∞ ）, where v is normal.

BOUNDEDNESS FROM BELOW OF MULTIPLICATION OPERATORS BETWEEN α-BLOCH SPACES ON THE UNIT BALL

In this article, we characterize the boundedness from below of multiplication operators between α-Bloch spaces on the unit ball.

A BOUNDARY SCHWARZ LEMMA FOR PLURIHARMONIC MAPPINGS FROM THE UNIT POLYDISK TO THE UNIT BALL

In this article, we present a Schwarz lemma at the boundary for pluriharmonic mappings from the unit polydisk to the unit ball, which generalizes classical Schwarz lemma for bounded harmonic functions to higher dimensions. It is proved that if the pluriharmonic mapping f ∈ P（Dn, BN） is C1＋α at z0 ∈ ErDn with f（0） = 0 and f（z0） = ω0∈BN for any n,N ≥ 1, then there exist a nonnegative vector λf =（λ1,0,…,λr,0,…,0）T∈R2 nsatisfying λi≥1/（22 n-1） for 1 ≤ i ≤ r such that where z’0 and w’0 are real versions of z0 and w0, respectively.

AVERAGE σ-WIDTHS OF THE UNIT BALL OF I_1~∞(R)IN I_2~∞(R)

In this paper we study the average σ-K width and the average σ-linear width of the unit ball of l;（R） inl;（R）. The exact values of these widths are calculated and an optimal subspace with the optimal linear opera-tor （for the σ- linear width） are identified.

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.

ATOMIC DECOMPOSITION OF μ-BERGMAN SPACE IN C^n

Let μ be a normal function on [0, 1）. The atomic decomposition of the μ-Bergman space in the unit ball B is given for all p 〉 0.

GLEASON'S PROBLEM ON THE SPACE F^(p,q,s)(B) IN C^(n)

Let Ω be a domain in C^(n) and let Y be a function space on Ω.If a∈Ω and g∈Y with g(a)=0,do there exist functions f_(1),f_(2),…,f_(n)∈Y such that g(z)=∑_(l=1)^(n)(z_(l)−a_(l))f_(l)(z)for all z=(z_(1),z_(2),…,z_(n))∈Ω?This is Gleason’s problem.In this paper,we prove that Gleason’s problem is solvable on the boundary general function space F^(p,q,s)(B)in the unit ball B of C^(n).

A Theorem of Nehari Type on the Bergman Space

In this paper we concern with the characterization of bounded linear operators S acting on the weighted Bergman spaces on the unit ball. It is shown that, if S satisfies the commutation relation STzi = Tzi（i =1,..,n）, where Tzi = zif and Tzi= P（zif） where P is the weighted Bergman projection, then S must be a Hankel operator.

Commuting Dual Toeplitz Operators on Weighted Bergman Spaces of the Unit Ball

In this paper, we study the commutativity of dual Toeplitz operators on weighted Bergman spaces of the unit ball. We obtain the necessary and sufficient conditions for the commutativity, essential commutativity and essential semi-commutativity of dual Toeplitz operator on the weighted Bergman spaces of the unit ball.

Riccati equations and Toeplitz-Berezin type symbols on Dirichlet space of unit ball

The present paper mainly gives some applications of Berezin type symbols on the Diriehlet space of unit ball. We study the solvability of some Riccati operator equations of the form XAX ＋ XB - CX = D related to harmonic Toeplitz operators on the Dirichlet space. Especially, the invariant subspaces of Toeplitz operators are also considered.

Bounded Projections and Duality on Spaces of Holomorphic Functions in the Unit Ball of (?)~n

In this paper three Banach spaces A(ф),A(ф)and A~1(ф)of functions holomor- phic in the unit ball B of ■~n are defined.We exhibit bounded projections from C(B)onto A(ф),from L~1(B)onto A~1(ф),and from L~∞(B)onto A(ф).Using these projections,we show that A(ф)~*≌A~1(ф)and A~1(ф)~*≌A(ф).

Equivalent Characterizations of α-Bloch Functions on the Unit Ball

In this paper we establish equivalent characterizations of α-Bloch functions on the unit ball without use of derivative, which generalize and improve the results of Nowak, Zhao, Wulan and Li.

A Boundary Schwarz Lemma for Holomorphic Mappings on the Polydisc

The authors prove a general Schwarz lemma at the boundary for holomorphic mappings from the polydisc to the unit ball in any dimensions.For the special case of one complex variable,the obtained results give the classic boundary Schwarz lemma.