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1
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Singularities in Muckenhoupt weighted function spaces

100%
Haroske D.
Banach Center Publications
|
2008
|
tom 79
|
nr 1
95-112
EN
We study weighted function spaces of Lebesgue, Besov and Triebel-Lizorkin type where the weight function belongs to some Muckenhoupt $𝓐_p$ class. The singularities of functions in these spaces are characterised by means of envelope functions.
2
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Lipschitz continuity in Muckenhoupt 𝓐₁ weighted function spaces

100%
Haroske D.
Banach Center Publications
|
2011
|
tom 92
|
nr 1
107-129
EN
We study continuity envelopes of function spaces $B^s_{p,q}(ℝⁿ,w)$ and $F^s_{p,q}(ℝⁿ,w)$ where the weight belongs to the Muckenhoupt class 𝓐₁. This essentially extends partial forerunners in [13, 14]. We also indicate some applications of these results.
3
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Traces of Besov spaces on fractal h-sets and dichotomy results

64%
Caetano A., Haroske D.
Studia Mathematica
|
2015
|
tom 231
|
nr 2
117-147
EN
We study the existence of traces of Besov spaces on fractal h-sets Γ with a special focus on assumptions necessary for this existence; in other words, we present criteria for the non-existence of traces. In that sense our paper can be regarded as an extension of Bricchi (2004) and a continuation of Caetano (2013). Closely connected with the problem of existence of traces is the notion of dichotomy in function spaces: We can prove that-depending on the function space and the set Γ-there occurs an alternative: either the trace on Γ exists, or smooth functions compactly supported outside Γ are dense in the space. This notion was introduced by Triebel (2008) for the special case of d-sets.
4
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Embeddings of Besov-Morrey spaces on bounded domains

64%
Haroske D., Skrzypczak L.
Studia Mathematica
|
2013
|
tom 218
|
nr 2
119-144
EN
We study embeddings of spaces of Besov-Morrey type, $id_{Ω}: 𝓝^{s₁}_{p₁,u₁,q₁}(Ω) ↪ 𝓝^{s₂}_{p₂,u₂,q₂}(Ω)$, where $Ω ⊂ ℝ^{d}$ is a bounded domain, and obtain necessary and sufficient conditions for the continuity and compactness of $id_{Ω}$. This continues our earlier studies relating to the case of $ℝ^{d}$. Moreover, we also characterise embeddings into the scale of $L_{p}$ spaces or into the space of bounded continuous functions.
5
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Embeddings of doubling weighted Besov spaces

64%
Haroske D., Skandera P.
Banach Center Publications
|
2014
|
tom 102
|
nr 1
105-119
EN
We study continuous embeddings of Besov spaces of type $B_{p,q}^s(ℝⁿ,w)$, where s ∈ ℝ, 0 < p < ∞, 0 < q ≤ ∞, and the weight w is doubling. This approach generalises recent results about embeddings of Muckenhoupt weighted Besov spaces. Our main argument relies on appropriate atomic decomposition techniques of such weighted spaces; here we benefit from earlier results by Bownik. In addition, we discuss some other related weight classes briefly and compare corresponding results.
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