We consider Green operators from the Boutet de Monvel algebra in Hölder–Zygmund spaces of variable smoothness on $\overline{\mathbb R}^{n}_+$. The order depends a point domain and may take negative values. sufficient conditions boundedness are obtained.

We study the relationship between sampling sequences in infinite dimensional Hilbert spaces of analytic functions and Marcinkiewicz-Zygmund inequalities subspaces polynomials. focus on Hardy space Bergman one variable because they provide two settings with a strikingly different behavior.

Abstract In this paper, we define the multilinear Calderón–Zygmund operators on differential forms and prove end-point weak type boundedness of operators. Based nonhomogeneous A -harmonic tensor, Poincaré-type inequalities for are obtained.

In the paper we consider Calderón-Zygmund operators in nonhomogeneous spaces. We are going to prove the analogs of classical results for homogeneous spaces. Namely, we prove that a Calderón-Zygmund operator is of weak type if it is bounded in L. We also prove several versions of Cotlar’s inequality for maximal singular operator. One version of Cotlar’s inequality (a simpler one) is proved in Eu...