If A is a Lipschitz function, i.e., || A |L < °°, then %A makes a very significant example of non-convolution type singular integral operators. The problem of L -boundedness of the Cauchy transform was raised and solved when || A |L is small by A. P. Calderόn in relation to the Dirichlet problem on Lipschitz domains [Call, Cal2]. Since then, it has been a central problem in the theory of singul...

the grace mission has provided scientific community time-variable gravity field solutions with high precision and on a global scale. the grace mission was launched on march 2003. this mission consists of two satellites that pursue each other in their orbit. distance between two satellites in orbit is measured continuously to an accuracy of better than 1 micron using kbr system placed in satelli...

We find the critical charge for a topologically massive gauge theory for any gauge group, generalising our earlier result for SU(2). The relation between critical charges in TMGT, singular vectors in the WZNW model and logarithmic CFT is investigated.

Abstract We develop product space theory of singular integrals with mild kernel regularity. study these regularity questions specifically in situations that are very tied to the T 1 type arguments and corresponding structural theory. In addition, our results multilinear.

Let (X, g) be a product cone with the metric $$g=dr^2+r^2h$$ , where $$X=C(Y)=(0,\infty )_r\times Y$$ and cross section Y is $$(n-1)$$ -dimensional closed Riemannian manifold (Y, h). We study upper boundedness of heat kernel associated operator $${\mathcal {L}}_V=-\Delta _g+V_0 r^{-2}$$ $$-\Delta _g$$ positive Friedrichs extension Laplacian on X $$V=V_0(y) $$V_0\in {\mathcal {C}}^\infty (Y)$$ r...

Second-kind Volterra integral equations with weakly singular kernels typically have solutions which are nonsmooth near the initial point of the interval of integration. Using an adaptation of the analysis originally developed for nonlinear weakly singular Fredholm integral equations, we present a complete discussion of the optimal (global and local) order of convergence of piecewise polynomial ...