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.     

Singular integral operators of near-product-type on the Heisenberg group

In this paper we establish Lp-boundedness (1<p<∞) for a class of singular convolution operators on the Heisenberg group whose kernels satisfy regularity and cancellation conditions adapted to the implicit (n+1)-parameter structure. The polyradial kernels of this type arose in [A.J. Fraser, An (n+1)-fold Marcinkiewicz multiplier theorem on the Heisenberg group, Bull. Austral. Math. Soc. 63 (2001) 35-58; A.J. Fraser, Convolution kernels of (n+1)-fold Marcinkiewicz multipliers on the Heisenberg group, Bull. Austral. Math. Soc. 64 (2001) 353-376] as the convolution kernels of (n+1)-fold Marcinkiewicz-type spectral multipliers m(L₁,…,Ln,iT) of the n-partial sub-Laplacians and the central derivative on the Heisenberg group. Thus they are in a natural way analogous to product-type Calderón-Zygmund convolution kernels on Rn. Here, as in [A.J. Fraser, An (n+1)-fold Marcinkiewicz multiplier theorem on the Heisenberg group, Bull. Austral. Math. Soc. 63 (2001) 35-58; A.J. Fraser, Convolution kernels of (n+1)-fold Marcinkiewicz multipliers on the Heisenberg group, Bull. Austral. Math. Soc. 64 (2001) 353-376], we extend to the (n+1)-parameter setting the methods and results of Müller, Ricci, and Stein in [D. Müller, F. Ricci, E.M. Stein, Marcinkiewicz multipliers and two-parameter structures on Heisenberg groups I, Invent. Math. 119 (1995) 199-233] for the two-parameter setting and multipliers m(L,iT) of the sub-Laplacian and the central derivative.     

Stein流形上Bochner-Martinelli型积分的导数的Plemelj公式

运用局部化方法和双全纯映射,通过Stein流形和C~n空间中Bochner-Martinelli核的联系,借助已获得的C~n空间中导数的Plemelj公式,得到Stein流形上导数的Plemelj公式.     

A generalization of Bendixson's criterion

Bendixson's condition on the nonexistence of periodic solutions for planar ordinary differential equations is extended to higher dimensional ordinary differential equations with first integrals to preclude the existence of certain invariant Lipschitz compact submanifolds for those equations.

     

Interionic forces in AgF,AgCl and AgBr crystals

An interionic force model has been used in which the short range nearest neighbour and the next nearest neighbour repulsive interactions and the van der Waals’ interactions are balanced by the long range electrostatic forces. The nearest neighbour and the next nearest neighbour interactions are derived from the overlap integrals for outer shell electrons. The van der Waals’ interactions are estimated from the Slater-Kirkwood variational method. The cohesive energy, the bulk modulus and its pressure dependence for AgF, AgCl and AgBr crystals have been calculated and compared with experimental data.     

On the Growth of Convergence Radii for the Eigenvalues of the Mathieu Equation

It is proved that the convergence radii ρn of the eigenvalues of the Mathieu equation satisfy lim inf ρn/n² > kk′K² = 2.0418., where the modulus k of the complete elliptic integrals is determined by 2E = K.     

Bounds for Relative Projection Constants in L 1 (-1,1)

For n -dimensional subspaces E _n , F _n of L ¹ (-1,1) with E _n spanned by Chebyshev polynomials of the second kind and F _n the set of Müntz polynomials with , , it is shown that the relative projection constants satisfy (E _n , L ¹ (-1,1)) C log n and (F _n , L ¹ (-1,1)) = O(1) , . The spaces L ¹ _w(α,β) , where w _α,β is the weight function of the Jacobi polynomials and , are also studied. The Jacobi partial sum projections, which are used in connection with E _n , are not minimal. September 26, 1996.     

Stochastic integrals of empirical-type processes with applications to censored regression

Motivated by the analysis of linear rank estimators and the Buckley-James nonparametric EM estimator in censored regression models, we study herein the asymptotic properties of stochastic integrals of certain two-parameter empirical processes. Applications of these results on empirical processes and their stochastic integrals to the asymptotic analysis of censored regression estimators are also given.     

一类Marcinkiewicz积分的L~p有界性

本文利用Fourier变换方法,在核函数缺乏光滑性的条件下,考虑Marcinkiewicz积分的L~2和加权L~p有界性,改进了[3]和[9]中的结论.