This paper deals with wavelet frames for a large class of distributions on euclidean n-space, including all compactly supported distributions. These representations characterize the global, local, and pointwise regularity of the distribution considered.
We prove invariance principles for partial sum processes in Besov spaces. This functional framework allows us to give a unified treatment of the step process and the smoothed process in the same parametric scale of function spaces. Our functional central limit theorems in Besov spaces hold for i.i.d. sequences and also for a large class of weakly dependent sequences.
In this paper we consider the following Dirichlet problem for elliptic systems: where is a Dirac operator in Euclidean space, is defined in a bounded Lipschitz domain in and takes value in Clifford algebras. We first introduce variable exponent Sobolev spaces of Clifford-valued functions, then discuss the properties of these spaces and the related operator theory in these spaces. Using the Galerkin method, we obtain the existence of weak solutions to the scalar part of the above-mentioned...
Let Ω be a bounded strictly pseudoconvex domain in . In this paper we find sufficient conditions on a function f defined on Ω in order that the weighted Bergman projection belong to the Hardy-Sobolev space . The conditions on f we consider are formulated in terms of tent spaces and complex tangential vector fields. If f is holomorphic then these conditions are necessary and sufficient in order that f belong to the Hardy-Sobolev space .
We study the continuity and compactness of embeddings for radial Besov and Triebel-Lizorkin spaces with weights in the Muckenhoupt class . The main tool is a discretization in terms of an almost orthogonal wavelet expansion adapted to the radial situation.
In this paper we give a general presentation of the homogenization of Neumann type problems in periodically perforated domains, including the case where the shape of the reference hole varies with the size of the period (in the spirit of the construction of self-similar fractals). We shows that -convergence holds under the extra assumption that there exists a bounded sequence of extension operators for the reference holes. The general class of Jones-domains gives an example where this result applies....
In this paper we give a general presentation of the homogenization of Neumann type problems in periodically perforated domains, including the case where the shape of the reference hole varies with the size of the period (in the spirit of the construction of self-similar fractals). We shows that H0-convergence holds under the extra assumption that there exists a bounded sequence of extension operators for the reference holes. The general class of Jones-domains gives an example where this result...