The boundedness of maximal operators and singular integrals via Fourier transform estimates

In this paper, the author studies the mapping properties for some general maximal operators and singular integrals on certain function spaces via Fourier transform estimates. Also, some concrete maximal operators and singular integrals are studied as applications.     

On the convergence of Filon quadrature

We analyze the convergence behavior of Filon-type quadrature rules by making explicit the dependence on both k, the parameter that controls the oscillatory behavior of the integrand, and n, the number of function evaluations. We provide explicit conditions on the domain of analyticity of the integrand to ensure convergence for n→∞.     

L p boundedness of Marcinkiewicz integrals with H 1 kernels

We establish the L^p boundedness of Marcinkiewicz integral operators with kernels in theHardy space on a compact submanifold of finite type. Previously such boundedness properties were obtained when the submanifold is a sphere. Our result shows that what matters is not the symmetry, but a certain type of curvature property of the submanifold.     

Evaluation of one-centre electron interaction integrals over slater type atomic orbitals

Simplified expressions for one-centre electron interaction integrals in general and Slater-Condon parameters as well as repulsion integrals of the type (aa|aa) in particular have been obtained over Slater-type atomic orbitals. Results calculated using these expressions are in agreement with those due to other authors.     

Log-Polynomial Period Functions for Hecke Groups

In this article we shall determine the automorphic integrals of positive and negative integral weight associated with the full modular group and some Hecke groups. This will be done by using the Hecke Correspondence. We will also give a characterization of multiplier systems of real weight for Hecke groups.     

Weighted endpoint estimates for commutators of Marcinkiewicz integrals

Let μΩ^mb be the commutator generalized by μΩ, the n-dimensional Marcinkiewicz integral, and b ∈ BMO（R^n）. The author establishes the weighted weak LlogL-type estimates for μΩ^mb when Ω satisfies a kind of Dini conditions, which improves the known result essentially.     

Inversion of the Kirkwood–Buff theory of solutions: application to binary systems

Kirkwood–Buff (K–B) integrals play an important role in characterizing the properties and interactions of various liquid mixtures. However, there exists no method to calculate directly the K–B integrals from the easily available experimental data of ultrasonic velocity and density. An attempt has been made to evaluate the same using these initial parameters. A statistical mechanical theory advanced by Arakawa et al. has been used here, in combination with a semi-empirical formula to compute K–B parameters in the whole concentration range for six binary systems at atmospheric pressure and at 298.15 K.     

Riesz transforms for a non-symmetric Ornstein-Uhlenbeck semigroup

Let (ℋ _t ) _t≥0 be the Ornstein-Uhlenbeck semigroup on ℝ ^d with covariance matrix I and drift matrix −λ(I+R), where λ>0 and R is a skew-adjoint matrix and denote by γ _∞ the invariant measure for (ℋ _t ) _t≥0. Semigroups of this form are the basic building blocks of Ornstein-Uhlenbeck semigroups which are normal on L ²(γ _∞). We investigate the weak type 1 estimate of the Riesz transforms for (ℋ _t ) _t≥0. We prove that if the matrix R generates a one-parameter group of periodic rotations then the first order Riesz transforms are of weak type 1 with respect to the invariant measure γ _∞. We also prove that the Riesz transforms of any order associated to a general Ornstein-Uhlenbeck semigroup are bounded on L ^p (γ _∞) if 1<p<∞. The authors have received support by the Italian MIUR-PRIN 2005 project “Harmonic Analysis” and by the EU IHP 2002-2006 project “HARP”.     

弱Hardy空间上的参数型Marcinkiewicz积分

证明了参数型Marcinkiewicz积分μΩ^p是（H^p,∞ , L^p,∞）（0〈p≤1）型的算子，这里Ω是满足Lipα条件的R^＊上的零次齐次函数．对于p=1，减弱了Ω的条件μΩ^p得到μΩ^p是（H^1,∞ , L^1,∞）型的．作为上述结果的推论，得到了μΩ^p是弱（1，1）型的算子．     

Cauchy integrals on Lipschitz surfaces in octonionic space

With the newly developed octonion analytic function theory, we confirm the octonionic analogue of the Calderón's conjecture. As application, we obtain the Plemelj formula in octonionic space.