Yakubovich, S. B.
Published in
Lithuanian Mathematical Journal

We prove the Plancherel theorem and establish related L2-properties for the following singular integral transformation associated with the product of Euler’s Gamma-functions: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgree...

Chen, Daning Chen, Jiecheng Fan, Dashan
Published in
Applied Mathematics-A Journal of Chinese Universities

The authors study the singular integral operator \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$T_{\Omega ,\alpha } f(x) = p.v.\int_{R^n } {b(\left| y \right|)\Omega ...

Popova, M. Gorbatikh, L.
Published in
Archive of Applied Mechanics

A problem of partial sliding along a planar crack with a local drop in frictional resistance is investigated. A sliding zone initiates in the area of reduced friction, and then propagates as the applied shear load is monotonously increased. The problem is formulated in general terms, and then solved for the case when sliding spreads as a penny-shap...

Lu, Shanzhen Wu, Qiang Yang, Dachun
Published in
Science in China Series A: Mathematics

Let [b,T] be the commutator of the functionb ∈ Lipβ(ℝn) (0

Ishihama, N.
Published in
International Journal of Fracture

The interaction problem of a kinked crack and the edges of a bending trapezoidal plate which takes the effects of transverse shear deformation into account is presented. The research method is based upon the complex potential technique of Muskhelishvili using conformal mapping. Furthermore, for the analysis of the moment intensities at the tips of ...

Ding, Yong Lu, Shanzhen
Published in
Science in China Series A: Mathematics

It is proved that a class of multilinear singular integral operators with homogeneous kernels are bounded operators from the product spaces\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt}...

Cowling, Michael Qian, Tao
Published in
Science in China Series A: Mathematics

The operaton on the n-complex unit sphere under study have three forms: the singular integrals with holomorphic kernels, the bounded and holomorphic Fourier multipliers, and the Cauchy-Dunford bounded and holomorphic functional calculus of the radial Dirac operator\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{a...

Anastassiou, George A. Gal, Sorin G.
Published in
Journal of Computational Analysis and Applications

In this article it is established that the well-known singular integrals of Picard, Poisson–Cauchy, Gauss–Weierstrass, and their Jackson-type generalizations fulfill the “global smoothness preservation” property, i.e., they “ripple” less than the function they are applied on, that is, producing a nice and fit approximation to the unit. The related ...

Lu, Shanzhen Tang, Lin Yang, Dachun
Published in
Science in China Series A: Mathematics

The boundedness on homogeneous Herz spaces is established for a large class of linear commutators generated by BMO(Rn) functions and linear operators of rough kernels which include the Calderón-Zygmund operators and the Ricci-Stein oRfiUatory singular integrals with rough kernels.

Fan, Dashan Lu, Shanzhen Yang, Dachun
Published in
Georgian Mathematical Journal

In this paper, by means of the theories of singular integrals and linear commutators, the authors establish the regularity in Morrey spaces of strong solutions to nondivergence elliptic equations with VMO coefficients.