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.     

SOME QUADRATURE FORMULAE FOR SINGULAR INTEGRALS

The Gauss-Legendre quadrature formulae had been extended to numerical evaluation for singular integrals by some authors. In 1970, S.R.Piessens obtained the formula     

ON MULTILINEAR FRACTIONAL INTEGRALS

§1 Introduction In this paper we consider the boundedness of the followingoperators T_α(A_1, …, A_m, f) (x)=∫_(IR~n) multiply from j=1 to m((R_(K_j+1)(A_j, x, y))/(|x-y|~K_j))f(y)/(|x-y|~(n-α))dy (1)     

OSCILLATORY SINGULAR INTEGRALS WITH VARIABLE ROUGH KERNEL,Ⅱ

Let n≥2. In this paper, the author establishes the L^2 (R^n)-boundedness of some oscillatory singular integrals with variable rough kernels by means of some estimates on hypergeometric functions and congqucnt hypergeometric funtions.     

OSCILLATORY SINGULAR INTEGRALS WITH VARIABLE ROUGH KERNEL, Ⅱ

Let n≥2. In this paper, the author establishes the L2 (Rx)-boundedness of some oscillatory singular integrals with variable rough kernels by means of some estimates on hyper geometric functions and confluent hyper geometric funtions.     

ON QUADRATURE FORMULAE FOR SINGULAR INTEGRALS OF ARBITRARY ORDER

Some quadrature formulae for the numerical evaluation of singular integrals of arbitrary order are established and both the estimate of remainder and the convergence of each quadrature formula derived here are also given.     

BOUNDEDNESS OF MAXIMAL SINGULAR INTEGRALS

The authors study the singular integrals under the Hormander condition and the measure not satisfying the doubling condition. At first, if the corresponding singular integral is bounded from L2 to itself, it is proved that the maximal singular integral is bounded from L∞to RBMO except that it is infinite μ-a.e. on Rd. A sufficient condition and a necessary condition such that the maximal singular integral is bounded from L2 to itself are also obtained. There is a small gap between the two conditions.     

WEIGHTED ESTIMATES FOR COMMUTATORS OF MULTILINEAR CALDERóN-ZYGMUND OPERATORS WITH NON-DOUBLING MEASURES

Let μ be a nonnegative Radon measure on Rd,which only satisfies the poly-nomial growth condition.Under this assumption,the authors obtain some weighted weak-type estimates for the commutators generated by the multilinear Calder'on-Zygmund operators and RBMO(μ) functions.     

L^P BOUNDS FOR SINGULAR INTEGRALS ASSOCIATED TO SURFACES OF REVOLUTION ON PRODUCT DOMAINS

In this paper, the authors establish Lp boundedness for several classes of multiple singular integrals along surfaces of revolution with kernels satisfying rather weak size condition. The results of the corresponding maximal truncated singular integrals are also obtained. The main results essentially improve and extend some known results.     

APPROXIMATION OF SINGULAR INTEGRALS BY INTERPOLATING SPLINES

In this paper we are mainly concerned with the approximation of the following type of singular Integrals: where w(t)≥0 is a weight function, f(x) a real continuous function on [a, b], satisfying certain smooth conditions, and the integral is of Canchy principal value.     

FOURIER TRANSFORMATION AND SINGULAR INTEGRALS ON SELF-SIMILAR MEASURE

This paper serves two purposes. One is to modify Strichartz's results with respect to theasymptotic averages of the Fourier transform of μ on , self-similar measure defined byHutchinson. Another purpose is to consider a singular integral operator on μ and show that this op-erator is of type (p,p)(1相似文献   

BOUNDEDNESS OF OSCILLATORY SINGULAR INTEGRALS ON HK_P SPACES

In this paper, we consider the HK boundedness for certain oscillatory singular integral operators.     

ON A MULTILINEAR OSCILLATORY SINGULAR INTEGRAL OPERATOR （I）

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EVALUATION OF SINGULAR AND NEARLY SINGULAR INTEGRALS IN THE BEM WITH EXACT GEOMETRICAL REPRESENTATION＊

The geometries of many problems of practical interest are created from circular or ellip- tic arcs. Arc boundary elements can represent these boundaries exactly, and consequently, errors caused by representing such geometries using polynomial shape functions can be removed. To fully utilize the geometry of circular boundary, the non-singular boundary integral equations （BIEs） and a general nonlinear transformation technique available for arc elements are introduced to remove or damp out the singular or nearly singular proper- ties of the integral kernels. Several benchmark 2D elastostatic problems demonstrate that the present algorithm can effectively handle singular and nearly singular integrals occur- ring in the boundary element method （BEM） for boundary layer effect and thin-walled structural problems. Owing to the employment of exact geometrical representation, only a small number of elements need to be divided along the boundary and high accuracy can be achieved without increasing other more computational efforts.     

WEIGHTED INEQUALITIES FOR MULTILINEAR POTENTIAL TYPE OPERATORS

The author derives a kind of weighted norm inequalities which relate the multilinear potential type integral operators to the corresponding maximal operators.     

WEIGHTED INEQUALITIES FOR MULTILINEAR POTENTIAL TYPE OPERATORS

The author derives a kind of weighted norm inequalities which relate the multilinear potential type integral operators to the corresponding maximal operators.     

POINTWISE ESTIMATES FOR CONVEX POLYNOMIAL APPROXIMATION

We are interested in approximating convex functions by convexpolynomials. The problem we concern is whether this kind of con-strained approximation can perform as well as unconstrained appro-ximation. There are several results showing the answers. Letf(x)∈C[-1,1], and π_n be the class of algebraic polynomials of     

SINGULAR INTEGRALS IN SEVERAL COMPLEX VARIABLES(Ⅱ)——HADAMARD PRINCIPAL VALUE ON A SPHERE

Hadamard introduced the concept of finite parts of divergent integrals.i.e.Hadamardprincipal value,when he researched the Cauehy problems of the hyperbolic type partialdifferential equations.In this paper,the authors try to generalize this concept to the singularintegrals on a sphere of several complex variables space C~n.The Hadamard principal valueof higher order singular integralis defined and the corresponding Plemelj formula is obtained.     

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.     

SINGULAR PERTURBATIONS FOR QUASILINEAR HYPERBOLIC EQUATIONS

This paper deals with the following mixed problem for Quasilinear hyperbolic equationsThe M order uniformly valid asymptotic solutions are obtained and there errors areestimated.