9 documents found, page 1 of 1

Nuclear and Compact Embeddings in Function Spaces of Generalised Smoothness

We study nuclear embeddings for function spaces of generalised smoothness defined on a bounded Lipschitz domain Ω ⊂ Rd. This covers, in particular, the well-known situation for spaces of Besov and Triebel–Lizorkin spaces defined on bounded domains as well as some first results for function spaces of logarithmic smoothness. In addition, we provide some new, more general approach to compact embeddings for such fu...

Wavelet decomposition and embeddings of generalised Besov–Morrey spaces

We study embeddings between generalised Besov–Morrey spaces Nφ,p,qs(Rd). Both sufficient and necessary conditions for the embeddings are proved. Embeddings of the Besov–Morrey spaces into the Lebesgue spaces Lr(Rd) are also considered. Our approach requires a wavelet characterisation of the spaces which we establish for the system of Daubechies wavelets. © 2021 The Author(s); The first and last author were part...

Spaces of generalized smoothness in the critical case: optimal embeddings, cont...

Continuity envelopes and sharp embeddings in spaces of generalized smoothness

We study continuity envelopes in spaces of generalized smoothness and . The results are applied in proving sharp embedding assertions in some limiting situations.; http://www.sciencedirect.com/science/article/B6WJJ-4RR86XB-2/1/6bcac204b3b58952d7b524c4599cb512

On some characterizations of Besov spaces of generalized smoothness

We present characterizations of the Besov spaces of generalized smoothness B(δ,N)p,q (Rn ) via approximation and by means of differences. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Growth envelopes of anisotropic function spaces

The present paper is devoted to the study of growth envelopes of anisotropic function spaces. An affirmative answer is given to the question of [19, Conjecture 13], whether the growth envelopes are independent of anisotropy. As an application, related anisotropic Hardy inequalities are presented and we also discuss a connection to some anisotropic fractal sets.; CMUC

Non-smooth atomic decompositions of anisotropic function spaces and some applic...

The main purpose of the present paper is to extend the theory of non-smooth atomic decompositions to anisotropic function spaces of Besov and Triebel-Lizorkin type. Moreover, the detailed analysis of the anisotropic homogeneity property is carried out. We also present some results on pointwise multipliers in special anisotropic function spaces.; CMUC; Junior Research Team Fractal analysis

Continuity envelopes of spaces of generalised smoothness, entropy and approxima...

We study continuity envelopes in spaces of generalised smoothness Bpq(s,[Psi]) and Fpq(s,[Psi]) and give some new characterisations for spaces Bpq(s,[Psi]). The results are applied to obtain sharp asymptotic estimates for approximation numbers of compact embeddings of type id:Bpq(s1,[Psi])(U)-->B[infinity][infinity]s2(U), where and U stands for the unit ball in . In case of entropy numbers we can prove two-side...

Local growth envelopes of spaces of generalized smoothness: the subcriticalcase

The concept of local growth envelope (εLGA, u) of the quasi-normed function space A is applied to the spaces of generalized smoothness B(s,psi) pq (Rn) and F(s,psi)pq (Rn) and it is shown that the influence of the function psi, which is a fine tuning of the main smoothness parameter s, is strong enough in order to show up in the corresponding growth envelopes. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)