We prove that the maximal functions associated with a Zygmund dilation dyadic structure in three-dimensional Euclidean space, and flag two-dimensional cannot be bounded by multiparameter sparse operators corresponding grid. also obtain supplementary results about absence of domination for strong function.

We study the Oseen problem with rotational e ect in exterior three-dimensional domains. Using a variational approach we prove existence and uniqueness theorems in anisotropically weighted Sobolev spaces in the whole three-dimensional space. As the main tool we derive and apply an inequality of the FriedrichsPoincaré type and the theory of Calderon-Zygmund kernels in weighted spaces. For the ext...

In this paper we characterize those functions f of the real line to itself such that the nonlinear superposition operator Tf defined by Tf [g] := f◦g maps the Hölder-Zygmund space Cs(Rn) to itself, is continuous, and is r times continuously differentiable. Our characterizations cover all cases in which s is real and s > 0, and seem to be novel when s > 0 is an integer.

We study the Oseen problem with rotational effect in exterior three-dimensional domains. Using a variational approach we prove existence and uniqueness theorems in anisotropically weighted Sobolev spaces in the whole three-dimensional space. As the main tool we derive and apply an inequality of the FriedrichsPoincaré type and the theory of Calderon-Zygmund kernels in weighted spaces. For the ex...

The classical paradigm of Calderon and Zygmund provides a set of techniques invariant under translations and dilations that allow to prove estimates for operators acting on function spaces on IR. We focus on the real line as underlying space and further concentrate on estimates for operators that are themselves invariant under translation and dilation. The only such operators bounded on L(R) ar...

The main thrust of this paper is to investigate the intimate link between the conformal group and singular integral operators, in particular, but not exclusively, operators of Calderón–Zygmund type, together with associated commutators acting on the L spaces of surfaces. Clifford analysis and Dirac operators are the basic tools used to help to unify these themes. These surfaces lie in euclidean...

Let [Formula: see text] be a generalized Calderón-Zygmund operator or [Formula: see text] ( the identity operator), let [Formula: see text] and [Formula: see text] be the linear operators, and let [Formula: see text]. Denote the Toeplitz type operator by [Formula: see text]where [Formula: see text] and [Formula: see text] is fractional integral operator. In this paper, we establish the sharp ma...

and Applied Analysis 3 Now we recall definitions and some properties of the Smirnov class, the Privalov class, the Bergman-Privalov class, and the Zygmund F-algebra on Bn or D. The space of all holomorphic functions on X Bn or D is denoted by H X . For each 0 < p ≤ ∞, the Hardy space is denoted by H X with the norm ‖ · ‖p. 2.1. Smirnov Class N∗ X Let X ∈ {Bn, Dn}. The Nevanlinna class N X on X ...