Entropy and approximation numbers of embeddings of function spaces with Muckenhoupt weights, II. General weights

Haroske, Dorothee D.; Skrzypczak, Leszek

doi:10.5186/aasfm.2011.3607

Cited by 48 publications

(48 citation statements)

References 35 publications

(41 reference statements)

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“…In [37] the above class of weights was extended to the class A loc p . We partly rely on our approaches [22][23][24][25].…”

Section: Function Spaces Of Type B Smentioning

confidence: 99%

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Spectral theory of some degenerate elliptic operators with local singularities

Haroske

Skrzypczak

2010

Journal of Mathematical Analysis and Applications

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This paper is based on our previous results (Haroske and Skrzypczak (2008) [23], Haroske and Skrzypczak (in press) [25]) on compact embeddings of Muckenhoupt weighted function spaces of Besov and Triebel-Lizorkin type with example weights of polynomial growth near infinity and near some local singularity. Our approach also extends [21]) in various ways. We obtain eigenvalue estimates of degeneratewhere the potential V may have singularities (in terms of Muckenhoupt weights), and A is a positive elliptic pseudodifferential operator of order > 0, self-adjoint in L 2 (R n ). This part essentially relies on the Birman-Schwinger principle. We conclude this paper with a number of examples, also comparing our results with preceding ones.

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“…In [37] the above class of weights was extended to the class A loc p . We partly rely on our approaches [22][23][24][25].…”

Section: Function Spaces Of Type B Smentioning

confidence: 99%

“…We dealt in [23][24][25] with a different approach and considered weights from the Muckenhoupt class A ∞ which -unlike 'admissible' weights -may have local singularities, that can influence embedding properties of such function spaces. Weighted Besov and Triebel-Lizorkin spaces with Muckenhoupt weights are well-known concepts, cf.…”

Section: Introductionmentioning

confidence: 99%

Spectral theory of some degenerate elliptic operators with local singularities

Haroske

Skrzypczak

2010

Journal of Mathematical Analysis and Applications

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“…This weight belongs to the class A loc 1 . It is known that w has singularity in 0, cf [4]. It means that sup Q∋0 w(Q) |Q| = ∞.…”

Section: Representation By Characteristic Functionsmentioning

confidence: 98%

Haar functions in weighted Besov and Triebel–Lizorkin spaces

Małecka

2015

Journal of Approximation Theory

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The paper deals with Haar wavelet bases in function spaces of Besov and Triebel-Lizorkin type with local Muckenhoupt weights. We show that Haar wavelets can be used to characterize such function spaces as far as absolute value of smoothness parameter is small enough and weights fulfill some conditions. The result is based on mapping properties of linear operators involving characteristic functions of dyadic cubes in related spaces and on local means characterization of weighted Besov and Triebel-Lizorkin spaces.

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“…This is an apparent modification of the weight

w_{ϰ, normalΓ}

, identifying Γ as the hyperplane

({} x \in R^{d} : x_{d} = 0)

and

α = ϰ \in R

. For further examples we refer to , , .…”

Section: Preliminariesmentioning

confidence: 99%

“…Let for

m \in {double-struckZ}^{d}

and

ν \in {double-struckN}_{0}, Q_{ν, m}

denote the d ‐dimensional cube with sides parallel to the axes of coordinates, centered at

2^{- ν} m

and with side length

2^{- ν}

. In we introduced the following notion of their set of singularities

{boldS}_{sing} false(w false)

. Definition For

w \in {scriptA}_{\infty}

we define the set of singularities

{boldS}_{sing} false(w false)

{boldS}_{sing} false(w false) = {boldS}_{0} false(w false) \cup {boldS}_{\infty} false(w false),

where

\begin{matrix} true \\ right S_{0} (w) & = & left ({} x \in R^{d} : \underset{Q_{ν, m} ∋ x}{trueprefixinf} \frac{w (Q_{ν, m})}{false| Q_{ν, m} false|} = 0), \\ right S_{\infty} (w) & = & left ({} x \in R^{d} : \underset{Q_{ν, m} ∋ x}{trueprefixsup} \frac{w (Q_{ν, m})}{false| Q_{ν, m} false|} = \infty) . \end{matrix}

…”

Section: Preliminariesmentioning

confidence: 99%

Embeddings of weighted Morrey spaces

Haroske

Skrzypczak

2016

Mathematische Nachrichten

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Entropy and approximation numbers of embeddings of function spaces with Muckenhoupt weights, II. General weights

Cited by 48 publications

References 35 publications

Spectral theory of some degenerate elliptic operators with local singularities

Spectral theory of some degenerate elliptic operators with local singularities

Haar functions in weighted Besov and Triebel–Lizorkin spaces

Embeddings of weighted Morrey spaces

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