We study a representation formula of the form ƒ=∑ Q< ƒ, ϑ Q> ψ Q for a distribution ƒ on R
n. This formula is obtained by discretizing and localizing a standard Littlewood-Paley …

During the last 60 years the theory of function spaces has been a subject of growing interest
and increasing diversity. Based on three formally different developments, namely, the theory …

Both the real-variable theory of function spaces and the boundedness of operators are
always one of the core contents of harmonic analysis, while the Lebesgue spaces are the …

There is a rapidly increasing number of papers dealing with smoothness spaces related to
Morrey spaces. It will be the aim of this survey to give an introduction to one of these …

A variety of results regarding multilinear Calderón-Zygmund singular integral operators is
systematically presented. Several tools and techniques for the study of such operators are …

We prove local‐in‐time unique existence and a blowup criterion for solutions in the Triebel‐
Lizorkin space for the Euler equations of inviscid incompressible fluid flows in ℝn, n≥ 2. As …

Nazarov, Treil and Volberg defined matrix $ A_p $ weights and extended the theory of
weighted norm inequalities on $ L^ p $ to the case of vector-valued functions. We develop …

Let $ b $ be a $ BMO $-function. It is well known that the linear commutator $[b, T] $ of a
Calderón-Zygmund operator $ T $ does not, in general, map continuously $ H^ 1 (\mathbb …

Let $ s\in {\mathbb R} $, $ q\in (0,\infty] $, and $\tau\in [0,\infty) $. It is well known that Besov-
type spaces $\dot B^{s,\tau} _ {p, q} $ with $ p\in (0,\infty] $ and Triebel--Lizorkin-type spaces …

This is the last one of three successive articles by the authors on matrix-weighted Besov-
type and Triebel--Lizorkin-type spaces $\dot B^{s,\tau} _ {p, q}(W) $ and $\dot F^{s,\tau} _ {p …