Operator-Valued Fourier Multipliers, Vector - Valued Besov Spaces, and Applications

1997 ◽  
Vol 186 (1) ◽  
pp. 5-56 ◽  
Author(s):  
Herbert Amann
Keyword(s):  
Besov Spaces ◽  
Fourier Multipliers ◽  
Vector Valued

scholarly journals Operator-valued Fourier multipliers on toroidal Besov spaces

2016 ◽  
Vol 50 (1) ◽  
pp. 109-137 ◽  
Author(s):  
Bienvenido Barraza Martínez ◽  
Iván González Martínez ◽  
Jairo Hernández Monzón
Keyword(s):  
Besov Spaces ◽  
Fourier Multipliers

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 Unimodular Fourier multipliers on homogeneous Besov spaces

2015 ◽  
Vol 425 (1) ◽  
pp. 536-547 ◽  
Author(s):  
Guoping Zhao ◽  
Jiecheng Chen ◽  
Dashan Fan ◽  
Weichao Guo
Keyword(s):  
Besov Spaces ◽  
Fourier Multipliers

scholarly journals Remarks on the Unimodular Fourier Multipliers onα-Modulation Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Guoping Zhao ◽  
Jiecheng Chen ◽  
Weichao Guo
Keyword(s):  
Besov Spaces ◽  
Fourier Multiplier ◽  
Radial Function ◽  
Necessary Conditions ◽  
Fourier Multipliers ◽  
Modulation Spaces ◽  
Multiplier Operator ◽  
Size Condition ◽  
Sufficient And Necessary Conditions ◽  
Fourier Multiplier Operator

We study the boundedness properties of the Fourier multiplier operatoreiμ(D)onα-modulation spacesMp,qs,α  (0≤α<1)and Besov spacesBp,qs(Mp,qs,1). We improve the conditions for the boundedness of Fourier multipliers with compact supports and for the boundedness ofeiμ(D)onMp,qs,α. Ifμis a radial functionϕ(|ξ|)andϕsatisfies some size condition, we obtain the sufficient and necessary conditions for the boundedness ofeiϕ(|D|)betweenMp1,q1s1,αandMp2,q2s2,α.

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.

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