We provide a full characterization in terms of the six parameters involved boundedness all standard weighted integral operators induced by harmonic Bergman-Besov kernels acting between different Lebesgue classes with weights on unit ball Rn. These some sense generalize projections. To obtain necessity conditions, we use technique that heavily depends precise inclusion relations and Bloch spaces...

In this paper an algorithm is presented for the regularization of singular integrals with any degrees of singularity, which may be employed in all three-dimensional problems analyzed by Boundary Elements. The integrals in Boundary Integrals Equations are inherently singular. For example, one can mention the integrals confronted in potential problems to evaluate the flow or the gradient of the f...

The monotone convergence theorem holds for the Riemann integral, provided (of course) it is assumed that the limit function is Riemann integrable. It might be thought, though, that this would be difficult to prove and inappropriate for an undergraduate course. In fact the identity is elementary: in the Lebesgue theory it is only the integrability of the limit function that is deep. This article...

In this paper an algorithm is presented for the regularization of singular integrals with any degrees of singularity, which may be employed in all three-dimensional problems analyzed by Boundary Elements. The integrals in Boundary Integrals Equations are inherently singular. For example, one can mention the integrals confronted in potential problems to evaluate the flow or the gradient of the f...

We compute point sets on the triangle that have low Lebesgue constant, with sixfold symmetries and Gauss-Legendre-Lobatto distribution on the sides, up to interpolation degree 18. Such points have the best Lebesgue constants among the families of symmetric points used so far in the framework of triangular spectral elements.

where T > 0 is a given number, a function f : [0, T ]× R → R satisfies certain regularity conditions and (Bt)t∈[0,T ] is a one dimensional Brownian motion on some probability space (Ω,Σ,P). Since in most cases explicit value of the integral (1) is not available, we must consider approximation schemes. We are interested in algorithms which use only discrete values of the driving Brownian motion ...