Characterization of a class of embeddings for function spaces with Muckenhoupt weights

Entropy and approximation numbers of embeddings of function spaces with Muckenhoupt weights, II. General weights.∗

We study compact embeddings for weighted spaces of Besov and TriebelLizorkin type where the weights belong to Muckenhoupt Ap classes. We focus our attention on the influence of singular points of the weights on the compactness of the embeddings as well as on the asymptotic behaviour of their entropy and approximation numbers.

A new class of function spaces on domains of R^d and its relations to classical function spaces

Scalar and Vector Muckenhoupt Weights

We inspect the relationship between the Ap,q condition for families of norms on vector valued functions and the Ap condition for scalar weights. In particular we will show if we are considering a norm-valued function ρ(·) such that, uniformly in all nonzero vectors x, ρ(·)(x) p ∈ Ap and ρ(·)(x) ∈ Aq then the following hold: If p = q = 2, and functions take values in R then ρ ∈ A2,2. If p = q = ...

Paraexponentials, Muckenhoupt Weights, and Resolvents of Paraproducts

We analyze the stability of Muckenhoupt’s RHdp and A d p classes of weights under a nonlinear operation, the λ-operation. We prove that the dyadic doubling reverse Hölder classes RHdp are not preserved under the λ-operation, but the dyadic doubling Ap classes A d p are preserved for 0 < λ < 1. We give an application to the structure of resolvent sets of dyadic paraproduct operators.

investigating the feasibility of a proposed model for geometric design of deployable arch structures

deployable scissor type structures are composed of the so-called scissor-like elements (sles), which are connected to each other at an intermediate point through a pivotal connection and allow them to be folded into a compact bundle for storage or transport. several sles are connected to each other in order to form units with regular polygonal plan views. the sides and radii of the polygons are...