scholarly journals Interpolation theorem for Nikol’skii-Besov type spaceswith mixed metric

2020 ◽  
Vol 100 (4) ◽  
pp. 33-42
Author(s):  
K.A. Bekmaganbetov ◽  
◽  
K.Ye. Kervenev ◽  
Ye. Toleugazy ◽  
◽  
...  
Keyword(s):  
Besov Space ◽  
Besov Spaces ◽  
Interpolation Theorem ◽  
Discrete Space ◽  
Mixed Derivative ◽  
Complex Interpolation ◽  
Interpolation Methods ◽  
Mixed Metric ◽  
Vector Valued

In this paper we study the interpolation properties of Nikol’skii-Besov spaces with a dominant mixed derivative and mixed metric with respect to anisotropic and complex interpolation methods. An interpolation theorem is proved for a weighted discrete space of vector-valued sequences l^α_q(A). It is shown that the Nikol’skii-Besov space under study is a retract of the space l^α_q(Lp). Based on the above results, interpolation theorems were obtained for Nikol’skii-Besov spaces with the dominant mixed derivative and mixed metric.

Interpolation of Morrey Spaces on Metric Measure Spaces

2014 ◽  
Vol 57 (3) ◽  
pp. 598-608 ◽  
Author(s):  
Yufeng Lu ◽  
Dachun Yang ◽  
Wen Yuan
Keyword(s):  
Interpolation Method ◽  
Interpolation Theorem ◽  
Morrey Spaces ◽  
Complex Interpolation ◽  
Metric Measure Spaces ◽  
Interpolation Methods ◽  
Measure Spaces

AbstractIn this article, via the classical complex interpolation method and some interpolation methods traced to Gagliardo, the authors obtain an interpolation theorem for Morrey spaces on quasimetric measure spaces, which generalizes some known results on ℝn.

Research about Influencing Factor on Interpolation Accuracy in Data Exchange of Fluid-Structure Interaction

2013 ◽  
Vol 318 ◽  
pp. 100-107
Author(s):  
Zhen Shen ◽  
Biao Wang ◽  
Hui Yang ◽  
Yun Zheng
Keyword(s):  
Data Exchange ◽  
Shape Function ◽  
Interpolation Method ◽  
Matching Condition ◽  
Optimal Interpolation ◽  
Complex Interpolation ◽  
Interpolation Function ◽  
Interpolation Methods ◽  
Interpolation Accuracy ◽  
Lower Accuracy

Six kinds of interpolation methods, including projection-shape function method, three-dimensional linear interpolation method, optimal interpolation method, constant volume transformation method and so on, were adoped in the study of interpolation accuracy. From the point of view about the characterization of matching condition of two different grids and interpolation function, the infuencing factor on the interpolation accuracy was studied. The results revealed that different interpolation methods had different interpolation accuracy. The projection-shape function interpolation method had the best effect and the more complex interpolation function had lower accuracy. In many cases, the matching condition of two grids had much greater impact on the interpolation accuracy than the method itself. The error of interpolation method is inevitable, but the error caused by the grid quality could be reduced through efforts.

Embedding vector-valued Besov spaces into spaces ofγ -radonifying operators

2008 ◽  
Vol 281 (2) ◽  
pp. 238-252 ◽  
Author(s):  
Nigel Kalton ◽  
Jan van Neerven ◽  
Mark Mark ◽  
Lutz Weis
Keyword(s):  
Besov Spaces ◽  
Vector Valued

scholarly journals Extended Cesáro operators between generalized Besov spaces and Bloch type spaces in the unit ball

2009 ◽  
Vol 7 (3) ◽  
pp. 209-223 ◽  
Author(s):  
Ze-Hua Zhou ◽  
Min Zhu
Keyword(s):  
Unit Ball ◽  
Besov Space ◽  
Besov Spaces ◽  
Complex Space ◽  
Bloch Space ◽  
Sufficient Conditions ◽  
Cesàro Operator ◽  
Type Spaces ◽  
Necessary And Sufficient ◽  
Cesaro Operator

Let 𝑔 be a holomorphic of the unit ballBin then-dimensional complex space, and denote byTgthe extended Cesáro operator with symbolg. Let 0 <p< +∞, −n− 1 <q< +∞,q> −1 and α > 0, starting with a brief introduction to well known results about Cesáro operator, we investigate the boundedness and compactness ofTgbetween generalized Besov spaceB(p, q)and 𝛼α- Bloch spaceℬαin the unit ball, and also present some necessary and sufficient conditions.

scholarly journals Interpolation methods to estimate eigenvalue distribution of some integral operators

2004 ◽  
Vol 2004 (9) ◽  
pp. 479-485
Author(s):  
E. M. El-Shobaky ◽  
N. Abdel-Mottaleb ◽  
A. Fathi ◽  
M. Faragallah
Keyword(s):  
Besov Space ◽  
Asymptotic Distribution ◽  
Function Space ◽  
Integral Operators ◽  
Eigenvalue Distribution ◽  
Factorization Theorem ◽  
Lizorkin Space ◽  
Interpolation Methods ◽  
Distribution Of Eigenvalues

We study the asymptotic distribution of eigenvalues of integral operatorsTkdefined by kernelskwhich belong to Triebel-Lizorkin function spaceFpuσ(F  qvτ)by using the factorization theorem and the Weyl numbersxn. We use the relation between Triebel-Lizorkin spaceFpuσ(Ω)and Besov spaceBpqτ(Ω)and the interpolation methods to get an estimation for the distribution of eigenvalues in Lizorkin spacesFpuσ(F  qvτ).

The Presentation of Biorthogonal Non-Tensor Trivariate Wavelet Wraps in Besov Space

2012 ◽  
Vol 461 ◽  
pp. 738-742
Author(s):  
De Lin Hua
Keyword(s):  
Besov Space ◽  
Frequency Analysis ◽  
Iteration Method ◽  
Filter Bank ◽  
Matrix Theory ◽  
Analysis Method ◽  
Analogy Method ◽  
Time Frequency ◽  
Orthonormal Bases ◽  
Vector Valued

In this paper, the concept of orthogonal non-tensor bivariate wavelet packs, which is the generalization of orthogonal univariate wavelet packs, is pro -posed by virtue of analogy method and iteration method. Their orthogonality property is investigated by using time-frequency analysis method and variable se-paration approach. Three orthogonality formulas regarding these wavelet wraps are established. Moreover, it is shown how to draw new orthonormal bases of space from these wavelet wraps. A procedure for designing a class of orthogonal vector-valued finitely supported wavelet functions is proposed by virtue of filter bank theory and matrix theory.

scholarly journals Weighted holomorphic Besov spaces on the polydisk

2011 ◽  
Vol 9 (1) ◽  
pp. 1-16 ◽  
Author(s):  
Anahit V. Harutyunyan ◽  
Wolfgang Lusky
Keyword(s):  
Fractional Derivative ◽  
Besov Space ◽  
Besov Spaces ◽  
Regular Variation ◽  
Holomorphic Functions ◽  
Spaces Of Holomorphic Functions ◽  
Weighted Besov Spaces ◽  
Unit Polydisk ◽  
Projection Theorems ◽  
Dimensional Lebesgue Measure

This work is an introduction of weighted Besov spaces of holomorphic functions on the polydisk. LetUnbe the unit polydisk inCnandSbe the space of functions of regular variation. Let1≤p<∞,ω=(ω1,…,ωn),ωj∈S(1≤j≤n)andf∈H(Un).The functionfis said to be an element of the holomorphic Besov spaceBp(ω)if‖f‖Bp(ω)p=∫Un|Df(z)|p∏j=1nωj(1-|zj|)/(1-|zj|2)2-pdm2n(z)<+∞, wheredm2n(z)is the2n-dimensional Lebesgue measure onUnandDstands for a special fractional derivative offdefined in the paper. For example, ifn=1thenDfis the derivative of the functionzf(z).We describe the holomorphic Besov space in terms ofLp(ω)space. Moreover projection theorems and theorems of the existence of a right inverse are proved.

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