THE EQUIVALENT CHARACTERIZATION OF F(p,q,s)SPACE ON BOUNDED SYMMETRIC DOMAINS OF Cn

LetΩ be a bounded symmetric domain in Cn. The purpose of this article is to define and characterize the general function space F（p, q, s） on Ω. Characterizing functions in the F（p, q, s） space is a work of considerable interest nowadays. In this article, the authors give several equivalent descriptions of the functions in the F（p, q, s） space on Ω in terms of fractional differential operators. At the same time, the authors give the relationship between F（p, q, s） space and Bloch type space on Ω too.

Compactness of Composition Operators from the p-Bloch Space to the q-Bloch Space on the Classical Bounded Symmetric Domains

In this paper, we introduce the weighted Bloch spaces on the first type of classical bounded symmetric domains , and prove the equivalence of the norms and . Furthermore, we study the compactness of composition operator from to , and obtain a sufficient and necessary condition for to be compact.

Some Estimates for the Fourier Transform on Rank 1 Symmetric Spaces

Two estimates useful in applications are proved for the Fourier transform in the space L^2(X), where X a symmetric space, as applied to some classes of functions characterized by a generalized modulus of continuity.

ANTICIPATING QUADRANT AND SYMMETRIC INTEGRALS IN THE PLANE WITH APPLICATION TO WIENER SPACE

We introduce anticipating quadrant and symmetric integrals in the plane, and establish the associated chain rules which are the same as the deterministic ones. In particular, we deduce the relation between quadrant integrals, symmetric integral, and Skorohod integral with respect to two-parameter Wiener processes.

A wideband fast multipole boundary element method for half-space/plane-symmetric acoustic wave problems

This paper presents a novel wideband fast multipole boundary element approach to 3D half-space/planesymmetric acoustic wave problems.The half-space fundamental solution is employed in the boundary integral equations so that the tree structure required in the fast multipole algorithm is constructed for the boundary elements in the real domain only.Moreover,a set of symmetric relations between the multipole expansion coefficients of the real and image domains are derived,and the half-space fundamental solution is modified for the purpose of applying such relations to avoid calculating,translating and saving the multipole/local expansion coefficients of the image domain.The wideband adaptive multilevel fast multipole algorithm associated with the iterative solver GMRES is employed so that the present method is accurate and efficient for both lowand high-frequency acoustic wave problems.As for exterior acoustic problems,the Burton-Miller method is adopted to tackle the fictitious eigenfrequency problem involved in the conventional boundary integral equation method.Details on the implementation of the present method are described,and numerical examples are given to demonstrate its accuracy and efficiency.

COMPACT COMPOSITION OPERATORS ON WEIGHTED BERGMAN SPACES ON BOUNDED SYMMETRIC DOMAINS

In this article, we borrow the idea of using Schur＇s test to characterize the compactness of composition operators on the weighted Bergman spaces in a bounded symmetricdomain Ω and verify that Cφ is compact on Lqa（Ω,dvβ）if and only if K（φ（z）,φ（z））/K（z,z）→0 as z→ Ω under a mild condition,where K（z,w）is the Bergman kernel.

OUTER OPERATORS FOR THE NONCOMMUTATIVE SYMMETRIC HARDY SPACES ASSOCIATED WITH FINITE SUBDIAGONAL ALGEBRA

In this article, we extended main results on outer operators of [6] to the symmetric Hardy spaces, when associated subdiagonal algebra is finite.

COMPLETE SPACE-LIKE SUBMANIFOLDS IN LOCALLY SYMMETRIC SEMI-DEFINITE SPACES

The purpose of this paper is to study complete space-like submanifolds with parallel mean curvature vector and flat normal bundle in a locally symmetric semi-defnite space satisfying some curvature conditions. We first give an optimal estimate of the Laplacian of the squared norm of the second fundamental form for such submanifold. Furthermore, the totally umbilical submanifolds are characterized.

Existence Theorem of the Multipliers on Riemannian Symmetric Space SL(3,H)/SP(3)

Using the method of Clerc and Stein study the multipliers of spherical Fourier transform on symmetric space to proof the multipliers theory for the space SL(3,H)/SP(3), completely avoid the complex theory of Anker, and we have gain the same result. Key words Riemannian symmetric space SL(3,H)/SP(3) - multipliers - spherical Fourier transform - invariant differential operator CLC number O 152.5 - O 186.12 Biography: LIAN Bao-sheng (1973-), male, Master, research direction: Li group and Lie algebra.

Linear Weingarten spacelike hypersurface in locally symmetric Lorentz space

The rigidity of spacelike hypersurface Mn immersed in locally symmetric space M1n+1 is investigated,where the(normalized)scalar curvature R and mean curvature H of Mn satisfy R=aH+b,and a,b are real constants.First,an estimate of the upper bound of the function L(nH)is given,where L is a second-order differential operator.Then,under the assumption that the square norm of the second fundamental form is bounded by a given positive constant,it is proved that Mn must be either totally umbilical or contain two distinct principle curvatures,one of which is simple.Moreover,a similar result is obtained for complete noncompact spacelike hypersurfaces in locally symmetric Einstein spacetime.Hence,some known rigidity results for hypersurface with constant scalar curvature are extended for the linear Weingarten case.

Ricci Symmetries of Static Space-Times with Maximal Symmetric Transverse Spaces

In the paper [M. Akbar and R.G. Cai, Commun. Theor. Phys. 45 （2006） 95], a complete classification is provided with at least one component of the vector field V is zero. In this paper, I consider the vector field V with all non-zero components and the static space times with maximal symmetric transverse spaces are classified according to their Ricci collineations. These are investigated for non-degenerate Ricci tensor det R ≠0. It turns out that the only collineations admitted by these spaces can be ten, seven, six or four. It also covers our previous results as a spacial case. Some new metrics admitting proper Ricci collineations are also investigated.

Ricci Collineations of Static Space Times with Maximal Symmetric Transverse Spaces

A complete classification of static space times with maximal symmetric transverse spaces is provided, according to their Ricci collineations. The classification is made when one component of Ricci collineation vector field V is non-zero （cases 1 - 4）, two components of V are non-zero （cases 5 - 10）, and three components of V are non-zero （cases 11 - 14）, respectlvily. Both non-degenerate （detRab ≠ 0） as well as the degenerate （det Rab = 0） cases are discussed and some new metrics are found.

Complete Spacelike Hypersurfaces with Constant Scalar Curvature in Locally Symmetric Lorentz Spaces

The complete space-like hypersurfaces with constant normal saclar curvature is discussed in a locally symmetric Lorentz space. A classified theorem is obtained by the operator L1 introduced by S Y Cheng and S T Yau [3].

A Model for a Spherically Symmetric Space Generated by a Spherical Gravitational Source and a Gravitational Medium with Constant Mass Density

A metric on a spherically symmetric space generated by a spherical source of gravity and filled with a gravitational medium is constructed, and criteria for the continuity of this metric on the entire space (which is equivalent to the absence of black holes) are found. Properties of radial geodesics under various constraints on the size of the gravitational source, its mass, and the mass density of the gravitational medium are studied.

Fixed Point Theorems in Cone Symmetric Spaces

In this paper, some common fixed point theorems for general occasionally weakly compatible selfmaps and non-selfmaps on cone symmetric spaces were proved. The interesting point of this paper is that we do not assume that the cone is solid. Our results generalize and complete the corresponding results in [9-15].

Weighted Bergman Spaces on Bounded Symmetric Domains

On bounded symmetric domain Ω of C^n, we investigate the properties of functions in weighted Bergman spaces A^P（Ω,dvs） for 0 〈 p ≤ ＋∞ and -1 〈 s 〈 4-∞. Based on the estimate of Bergman kernel, we obtain some characterizations of functions in A^P（Ω, dvs） in terms of a class of linear operators D^αB. Making use of these characterizations, we extend A^P（Ω,dvs） to the weighted Bergman spaces Aα^p,B（Ω,dvs） in a very natural way for 1 〈 p 〈 4-∞ and any real number s, that is, -∞ 〈 s 〈 ＋∞. This unified treatment covers some classical Bergman spaces, Besov spaces and Bloch spaces. Meanwhile, the boundedness of Bergman projection operators on Aα^P,β（Ω, dvs） and the dual of Aα^P,B（Ω, dvs） are given.

SPHERICAL SYMMETRIC SOLUTIONS FOR THE MOTION OF RELATIVISTIC MEMBRANES AND NULL MEMBRANES IN THE REISSNER-NORDSTRM SPACE-TIME

In this article, we concern the motion of relativistic membranes and null mem- branes in the Reissner-Nordstrom space-time. The equation of relativistic membranes moving in the Reissner-Nordstrom space-time is derived and some properties are discussed. Spherical symmetric solutions for the motion are illustrated and some interesting physical phenomena are discovered. The equations of the null membranes are derived and the exact solutions are also given. Spherical symmetric solutions for null membranes are just the two horizons of Reissner-NordstrSm space-time.

Chen’s Inequalities for Submanifolds in (<i>&kgreen;, &#181</i>)-Contact Space Form with a Semi-Symmetric Non-Metric Connection

In this paper, we obtain Chen’s inequalities in (k,?μ)-contact space form with a semi-symmetric non-metric connection. Also we obtain the inequalites for Ricci and K-Ricci curvatures.

Common Fixed Point Results for Occasionally Weakly Compatible Maps in G-Symmetric Spaces

The notion of a G-symmetric space is introduced and the common fixed points for some pairs of occasionally weakly compatible maps satisfying some contractive conditions in a G-symmetric space are proved. The results extend and improve some results in literature.

ANALYTICAL SOLUTION OF AXIAL SYMMETRICAL WALL TEMPERATURE DISTRIBUTION FOR HOLLOW CYLINDER

Using the variable transformation method,the formulae of the axial symmetrical wall temperature distribution during steady heat conduction of a hollow cylinder are derived in this paper.The wall temperature distribution and the wall heat flux distribution in both axial and radial direction can be calculated by the temperature distribution of the liquid medium both inside and outside the cylinder with temperature changing in axial direction.The calculation results are almost consistent with the experience results.The applicative condition of the formulae in this paper consists with most of practice.They can be applied to the engineering calculation of the steady heat conduction.The calculation is simple and accurate.