Smoothness Morrey Spaces of regular distributions, and some unboundedness property

Haroske, Dorothee D.; Moura, Susana D.; Skrzypczak, Leszek

doi:10.1016/j.na.2016.03.005

Cited by 18 publications

(30 citation statements)

References 26 publications

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“…For us it is interesting to know that in some cases the spaces N s u,p,q (R d ) also contain singular distributions. The following result is a combination of theorem 3.3 and theorem 3.4. from [4] and theorem 3.4. from [5].…”

Section: Definition and Basic Properties Of Besov-morrey Spacesmentioning

confidence: 89%

Besov-Morrey spaces and differences (extended version)

Hovemann

2020

Preprint

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Section: Definition and Basic Properties Of Besov-morrey Spacesmentioning

confidence: 89%

Besov-Morrey spaces and differences (extended version)

Hovemann

2020

Preprint

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“…Embeddings within spaces in this latter scale as well as to classical spaces like C(Ω) or L r (Ω) were investigated in [12,13]. In [8] we studied the question under what assumptions these spaces consist of regular distributions only.…”

Section: Function Spaces On Domainsmentioning

confidence: 99%

Entropy numbers of compact embeddings of smoothness Morrey spaces on bounded domains

Haroske

Skrzypczak

2020

Journal of Approximation Theory

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We study the compact embedding between smoothness Morrey spaces on bounded domains and characterise its entropy numbers. Here we discover a new phenomenon when the difference of smoothness parameters in the source and target spaces is rather small compared with the influence of the fine parameters in the Morrey setting. In view of some partial forerunners this was not to be expected till now. Our argument relies on wavelet decomposition techniques of the function spaces and a careful study of the related sequence space setting. , extended by M ∞,∞ (R d ) = L ∞ (R d ). In a parallel way one can define the spaces M ∞,p (R d ), p ∈ (0, ∞), but using the Lebesgue differentiation theorem, one arrives at M ∞,p (R d ) = L ∞ (R d ). Moreover, M u,p (R d ) = {0} for u < p, and for 0 < p 2 ≤ p 1 ≤ u < ∞,Now we present the smoothness spaces of Morrey type in which we are interested. The Schwartz space S(R d ) and its dual S ′ (R d ) of all complex-valued tempered distributions have their usual meaning here. Let ϕ 0 = ϕ ∈ S(R d ) be such that supp ϕ ⊂ y ∈ R d : |y| < 2 and ϕ(x) = 1 if |x| ≤ 1 ,

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“…For instance, embeddings within the scale of spaces A s u, p,q (Ω) as well as to classical spaces like C(Ω) or L r (Ω) were investigated in [14,15]. In [12] we studied the question under what assumptions these spaces consist of regular distributions only. Moreover, in [43] we considered the approximation numbers of some special compact embedding of A s,τ p,q (Ω) into L ∞ (Ω).…”

Section: Remark 211mentioning

confidence: 99%

“…where re : A s,τ p,q (R d ) → A s,τ p,q (Ω) is the restriction operator as above. Moreover, in [9] we studied the question under what assumptions these spaces consist of regular distributions only.…”

Section: Spaces On Domainsmentioning

confidence: 99%

Compact embeddings in Besov-type and Triebel–Lizorkin-type spaces on bounded domains

2020

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We study embeddings of Besov-type and Triebel-Lizorkin-type spaces, id τ : B s 1 ,τ 1 p 1 ,q 1 (Ω) → B s 2 ,τ 2 p 2 ,q 2 (Ω) and id τ : F s 1 ,τ 1 p 1 ,q 1 (Ω) → F s 2 ,τ 2 p 2 ,q 2 (Ω), where Ω ⊂ R d is a bounded domain, and obtain necessary and sufficient conditions for the compactness of id τ. Moreover, we characterize its entropy and approximation numbers. Surprisingly, these results are completely obtained via embeddings and the application of the corresponding results for classical Besov and Triebel-Lizorkin spaces as well as for Besov-Morrey and Triebel-Lizorkin-Morrey spaces.

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Smoothness Morrey Spaces of regular distributions, and some unboundedness property

Cited by 18 publications

References 26 publications

Besov-Morrey spaces and differences (extended version)

Besov-Morrey spaces and differences (extended version)

Entropy numbers of compact embeddings of smoothness Morrey spaces on bounded domains

Compact embeddings in Besov-type and Triebel–Lizorkin-type spaces on bounded domains

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