THE PROBLEM OF PARAMETRIC INTEGRATION TO THE SLIP LINE FIELD IN THE COMPRESSION OF THICK WORKPIECE

An integration depending on a parameter to the compression of a thick workpiece has been obtained. For the conventional prevailing numerical formulaa definite functional relationship bet-ween and y is found. Therefore a parametric integration can be used to get an analytical solution. Take the slip line field for l/h= 0.121 as an example, the analytical solution is basically the same as the prevailing numerical one. It is justified theoretically that for the slip line field a parametric integration is perfectly possible for a satisfactory analytical solution.

Multiple parametric Marcinkiewicz integrals with mixed homogeneity along surfaces

In this paper, the multiple parametric Marcinkiewicz integral operators with mixed homogeneity along surfaces are studied. The Lp-mapping properties for such operators are obtained under the rather weakened size conditions on the integral kernels both on the unit sphere and in the radial direction. The main results essentially improve and extend certain previous results.

An Integration Depending on Parameter Ф for Analytical Solution of the Compression of Thin Workpiece

An integration depending on the parameter Ф has been applied to the function Фdx so that an explicit formula of specific pressure calculation and an analytical solution are obtained.It has been found that the analytical solution is basically the same as the prevailing numerical one which is from the formula There- fore,it is justified theoretically that for the slip line field in the compression of a thin workpiece a parametric integra- tion is perfectly possible for satisfactory analytical solution.

WEIGHTED BOUNDEDNESS OF PARAMETRIC MARCINKIEWICZ INTEGRAL AND HIGHER ORDER COMMUTATOR

In this paper, the weighted boundedness of parametric Marcinkiewicz integral and its commutator with rough kernels are considered. In addition, the weak type norm inequalities for parametric Marcinkiewicz integral and its commutator with different weight functions and Dini kernel are also discussed.

Estimates for parametric Marcinkiewicz integrals in BMOand Campanato spaces

In this paper, the authors consider the behaviors of a class of parametricMarcinkiewicz integrals μ_Ω~ρ, μ_（Ω,）^（＊,）~ρ_λ and μ_Ω~ρ,S on BMO（Rn） and Campanato spaces with com-plex parameter ρ and the kernel Ω in Llog~＋ L（S^（n-1））. Here μ_（Ω,）^（＊,）~ρ_λand μ_Ω~ρ,S are parametricMarcinkiewicz functions corresponding to the Littlewood-Paley g_λ~＊-function and the Lusin areafunction S, respectively. Under certain weak regularity condition on Ω, the authors prove thatif f belongs to BMO（Rn） or to a certain Campanato space, then [μ_（Ω,）^（＊,）~ρ_λ（f）]~2, [μ_Ω~ρ,_S（f）]~2 and[μ_Ω~ρ（f）]~2 are either infinite everywhere or finite almost everywhere, and in the latter case, somekind of boundedness are also established.

Estimates of Some Integral Operators with Bounded Variable Kernels on the Hardy and Weak Hardy Spaces over R^n

In this paper,we first introduce Lσ1-（log L）σ2 conditions satisfied by the variable kernelsΩ（x,z） for 0≤σ1≤1 and σ2≥0.Under these new smoothness conditions,we will prove the boundedness properties of singular integral operators TΩ,fractional integrals TΩ,α and parametric Marcinkiewicz integrals μΩρ with variable kernels on the Hardy spaces Hp（Rn） and weak Hardy spaces WHP（Rn）.Moreover,by using the interpolation arguments,we can get some corresponding results for the above integral operators with variable kernels on Hardy-Lorentz spaces Hp,q（Rn） for all p 〈 q 〈 ∞.

A Class of Maximal Functions with Oscillating Kernels

The author studies the L^p mapping properties of a class of maximal functions that are related to oscillatory singular integral operators. Lp estimates, as well as the corresponding weighted estimates of such maximal functions, are obtained. Moreover, several applications of our results are highlighted.