In this article, the authors introduce Besov-type spaces with variable smoothness and
integrability. The authors then establish their characterizations, respectively, in terms of φ …

In this article, the authors first introduce the Triebel--Lizorkin-type space $ F_ {p (\cdot), q
(\cdot)}^{s (\cdot),\phi}(\mathbb R^ n) $ with variable exponents, and establish its $\varphi …

In this article, the authors first establish the pointwise characterizations of Besov and Triebel—
Lizorkin spaces with generalized smoothness on ℝ n via the Hajłasz gradient sequences …

In this paper we introduce Besov–Morrey spaces with all indices variable and study some
fundamental properties. This includes a description in terms of Peetre maximal functions and …

In this article we study atomic and molecular decompositions in 2-microlocal Besov and
Triebel–Lizorkin spaces with variable integrability. We show that, in most cases, the …

On 2-microlocal spaces with all exponents variable - ScienceDirect Skip to main contentSkip
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A new Besov space of variable smoothness is introduced on which the norm is defined in
terms of difference relations. This space is shown to be the trace of a weighted Sobolev …

This article is devoted to the study of variable 2-microlocal Besov-type and Triebel–Lizorkin-
type spaces. These variable function spaces are defined via a Fourier-analytical approach …

The paper is concerned with Besov spaces of variable smoothness B p, q φ 0 (R n,{tk}), in
which the norms are defined in terms of convolutions with smooth functions. A relation is …

In this paper we provide non-smooth atomic decompositions of 2-microlocal Besov-type and
Triebel–Lizorkin-type spaces with variable exponents B p (·), q (·) w, ϕ (R n) and F p (·), q (·) …