LIPSCHITZ ESTIMATES FOR MULTILINEAR SINGULAR INTEGRALS, II

In this paper, the authors study two classes of multilinear singular integralsand obtain their boundedness from Lebesgue spaces to Lipschitz spaces and from Herztype spaces to central Campanato spaces. Moreover, the authors also consider the extremecases.     

带Dini核的多线性算子在Herz型Hardy空间上的估计

In this paper, the authors study the multilinear operators with Dini Kernel and obtain their boundedness from Herz spaces to Herz-type Hardy spaces. Moreover, the authors also consider the corresponding fractional operators.     

Boundedness of commutators on Hardy type spaces

Let [b, T] be the commutator of the function b ∈ Lipβ(Rn) (0 ＜β≤ 1) and the CalderónZygmund singular integral operator T. The authors study the boundedness properties of [b, T] on the classical Hardy spaces and the Herz-type Hardy spaces in non-extreme cases. For the boundedness of these commutators in extreme cases, some characterizations are also given. Moreover, the authors prove that these commutators are bounded from Hardy type spaces to the weak Lebesgue or Herz spaces in extreme cases.     

Some Oscillatory Singular Integrals on Herz-type Spaces (Ⅱ)

In this paper, the authors prove that some oscillatory singular integral operators of non-convolution type with non-polynomial phases are bounded from the Herz-type Hardy spaces to the Herz spaces and from the Hardy spaces associated with the Beurling algebras to the Beurling algebras in higher dimensions, even though it is well-known that these operators are not bounded from the Hardy space H1(Rn) into the Lebesgue spaceL1(Rn).     

Statistical Structures on Metric Path Spaces

The authors extend the notion of statistical structure from Riemannian geometry to the general framework of path spaces endowed with a nonlinear connection and a generalized metric. Two particular cases of statistical data are defined. The existence and uniqueness of a nonlinear connection corresponding to these classes is proved. Two Koszul tensors are introduced in accordance with the Riemannian approach. As applications, the authors treat the Finslerian (α, β)-metrics and the Beil metrics used in relativity and field theories while the support Riemannian metric is the Fisher-Rao metric of a statistical model.     

A Survey of the Homotopy Properties of Inclusion of Certain Types of Configuration Spaces into the Cartesian Product

Let X be a topological space.In this survey the authors consider several types of configuration spaces,namely,the classical(usual)configuration spaces F_n(X)and D_n(X),the orbit configuration spaces F_n~G(X)and F_n~G(X)/S_nwith respect to a free action of a group G on X,and the graph configuration spaces F_n~Γ(X)and F_n~Γ(X)/H,whereΓis a graph and H is a suitable subgroup of the symmetric group S_n.The ordered configuration spaces F_n(X),F_n~G(X),F_n~Γ(X)are all subsets of the n-fold Cartesian product ∏_1~nX of X with itself,and satisfy F_n~G(X)?F_n(X)?F_n~Γ(X)?∏_1~nX.If A denotes one of these configuration spaces,the authors analyse the difference between A and ∏_1~nXfrom a topological and homotopical point of view.The principal results known in the literature concern the usual configuration spaces.The authors are particularly interested in the homomorphism on the level of the homotopy groups of the spaces induced by the inclusionι:A-→∏_1~nX,the homotopy type of the homotopy fibre I_ιof the mapιvia certain constructions on various spaces that depend on X,and the long exact sequence in homotopy of the fibration involving I_ιand arising from the inclusionι.In this respect,if X is either a surface without boundary,in particular if X is the 2-sphere or the real projective plane,or a space whose universal covering is contractible,or an orbit space S~k/Gof the k-dimensional sphere by a free action of a Lie group G,the authors present recent results obtained by themselves for the first case,and in collaboration with Golasi′nski for the second and third cases.The authors also briefly indicate some older results relative to the homotopy of these spaces that are related to the problems of interest.In order to motivate various questions,for the remaining types of configuration spaces,a few of their basic properties are described and proved.A list of open questions and problems is given at the end of the paper.     

COMPOSITION OPERATORS BETWEEN SOME WEIGHTED HARDY SPACES

Let D be the unit disc and H(D) be the set of all analytic functions on D. In [2], C. Cowen defined a space H = f ∈ H(D) : f(z) =sum from k=o to ∞ ak(z + 1)k, z∈ D, ‖f‖2 = sum from k=o to ∞ |ak|24k < ∞In this article, the authors consider the similar Hardy spaces with arbitrary weights and discuss some properties of them. Boundedness and compactness of composition operators between such spaces are also studied.     

Strongly Gauduchon Spaces

The authors define strongly Gauduchon spaces and the class■■, which are generalization of strongly Gauduchon manifolds in complex spaces. Comparing with the case of Kahlerian, the strongly Gauduchon space and the class■are similar to the Kahler space and the Fujiki class■■ respectively. Some properties about these complex spaces are obtained. Moreover, the relations between the strongly Gauduchon spaces and the class■■ are studied.     

叙列空间上的二级囿变函数I

The Stieltjes integral and bounded variation function of order 2 were introduced by Min, S. H., Guo Dajun and etc. One of the authors introduced the notion of bounded variation function on the sequence spaces, again. In this paper we consider the variation function of order 2 and the bounded variation function of order 2 from [α, b] to sequence space λ .     

TRACTABILITY OF MULTIVARIATE INTEGRATION PROBLEM FOR PERIODIC CONTINUOUS FUNCTIONS

The authors study the tractability and strong tractability of a multivariate integration problem in the worst case setting for weighted l-periodic continuous functions spaces of d coordinates with absolutely convergent Fourier series.The authors reduce the initial error by a factor ε for functions from the unit ball of the weighted periodic contin- uous functions spaces.Tractability is the minimal number of function samples required to solve the problem in polynomial in ε~(-1)and d.and the strong tractability is the pres- ence of only a polynomial dependence in ε.This problem has been recently studied for quasi-Monte Carlo quadrature rules.quadrature rules with non-negative coefficients. and rules for which all quadrature weights are arbitrary for weighted Korobov spaces of smooth periodic functions of d variables.The authors show that the tractability and strong tractability of a multivariate integration problem in worst case setting hold for the weighted periodic continuous functions spaces with absolutely convergent Fourier series under the same assumptions as in Ref.[14]on the weights of the Korobov space for quasi-Monte Carlo rules and rules for which all quadrature weights are non-negative.The arguments are not constructive.     

Convolutions,Tensor Products and Multipliers of the Orlicz-Lorentz Spaces

In this paper, the authors first give the properties of the convolutions of OrliczLorentz spaces Λ1,wand Λ2,won the locally compact abelian group. Secondly, the authors obtain the concrete representation as function spaces for the tensor products of Orlicz-Lorentz spaces Λ1,wand Λ2,w, and get the space of multipliers from the spaceΛ1,wto the space M2*,w. Finally, the authors discuss the homogeneous properties for the Orlicz-Lorentz space Λp,q,w.     

TOEPLITZ OPERATORS FROM HARDY SPACES TO WEIGHTED BERGMAN SPACES IN THE UNIT BALL OF Cn

We study Toeplitz operators from Hardy spaces to weighted Bergman spaces in the unit ball of Cⁿ.Toeplitz operators are closely related to many classical mappings,such as composition operators,the Volterra type integration operators and Carleson embeddings.We characterize the boundedness and compactness of Toeplitz operators from Hardy spaces H^p to weighted Bergman spaces A_α^q for the different values of p and q in the unit ball.     

Maximal Operators of Multilinear Singular Integrals on Weighted Hardy Type Spaces*

In this paper, the authors show that the maximal operators of the multilinear Calderón-Zygmund singular integrals are bounded from a product of weighted Hardy spaces into a weighted Lebesgue spaces, which essentially extend and improve the previous known results obtained by Grafakos and Kalton(2001) and Li, Xue and Yabuta(2011). The corresponding estimates on variable Hardy spaces are also established.     

Carleson Measures on the Weighted BergmanSpaces with B´ekoll´e Weights*

In this paper, the authors characterize Carleson measures for the weighted Bergman spaces with B′ekoll′e weights on the unit ball. They apply the Carleson embedding theorem to study the properties of Toeplitz-type operators and composition operators acting on such spaces.     

APPLICATIONS OF HERZ-TYPE TRIEBEL-LIZORKIN SPACES

In this paper, the authors first establish the connections between the Herz-type Triebel-Lizorkin spaces and the well-known Herz-type spaces; the authors then studythe pointwise multipliers for the Herz-type Triebel-Lizorkin spaces and show that pseudo-differential operators are bounded on these spaces by using pointwise multipliers.     

Absolutely summing multipliers on abstract Hardy spaces

We study summing multipliers from Banach spaces of analytic functions on the unit disc of the complex plane to the complex Banach sequence lattices. The domain spaces are abstract variants of the classical Hardy spaces generated by the complex symmetric spaces. Applying interpolation methods, we prove the Hausdorff Young and Hardy-Littlewood type theorems. We show applications of these results to study summing multipliers from the Hardy-Orlicz spaces to the Orlicz sequence lattices. The obtained results extend the well-known results for the Hp spaces.     

A NOTE TO OSCILLATORY SINGULAR INTEGRALS ON HERZ—TYPE SPACES

In this paper, we want to improve our previous results. We prove that some oscillatory strong singular integral operators of non-convolution type with non-polynomial phases are bounded from Herz-type Hardy spaces to Hertz spaces and from Hardy spaces associated with the Beurling algebras to the Beurling algebrasin higher dimensions.     

Bilinear pseudo-differential operators on local hardy spaces

In this paper, the authors consider a class of bilinear pseudo-differential operators with symbols of order 0 and type (1, 0) in the sense of Ho¨rmander and use the atomic decompositions of local Hardy spaces to establish the boundedness of the bilinear pseudo-differential operators and the bilinear singular integral operators on the product of local Hardy spaces.     

Parabolic equations with VMO coefficients in generalized Morrey spaces

In this paper, the authors establish the regularity in generalized Morrey spaces of solutions to parabolic equations with VMO coefficients by means of the theory of singular integrals and linear commutators.