Hörmander Fourier multiplier theorems with optimal regularity in bi-parameter Besov spaces

2021 ◽  
Vol 28 (4) ◽  
pp. 1047-1084
Author(s):  
Jiao Chen ◽  
Liang Huang ◽  
Guozhen Lu
Keyword(s):  
Besov Spaces ◽  
Fourier Multiplier ◽  
Optimal Regularity ◽  
Multiplier Theorems

OPERATOR-VALUED FOURIER MULTIPLIER THEOREMS ON TRIEBEL SPACES

2005 ◽  
Vol 25 (4) ◽  
pp. 599-609 ◽  
Author(s):  
Shangquan Bu ◽  
Jin-Myong Kim
Keyword(s):  
Fourier Multiplier ◽  
Multiplier Theorems

scholarly journals Operator-valued multiplier theorems characterizing Hilbert spaces

2004 ◽  
Vol 77 (2) ◽  
pp. 175-184 ◽  
Author(s):  
Wolfgang Arendt ◽  
Shangquan Bu
Keyword(s):  
Banach Space ◽  
Hilbert Space ◽  
Hilbert Spaces ◽  
Fourier Multiplier ◽  
Multiplier Theorem ◽  
Multiplier Theorems

AbstractWe show that the operator-valued Marcinkiewicz and Mikhlin Fourier multiplier theorem are valid if and only if the underlying Banach space is isomorphic to a Hilbert space.

scholarly journals On vector-valued Fourier multiplier theorems

1989 ◽  
Vol 93 (3) ◽  
pp. 201-222 ◽  
Author(s):  
Frank Zimmermann
Keyword(s):  
Fourier Multiplier ◽  
Multiplier Theorems ◽  
Vector Valued

Well-posedness of fractional degenerate differential equations in Banach spaces

2019 ◽  
Vol 22 (2) ◽  
pp. 379-395
Author(s):  
Shangquan Bu ◽  
Gang Cai
Keyword(s):  
Differential Equation ◽  
Fourier Multiplier ◽  
Sufficient Conditions ◽  
Complex Banach Space ◽  
Linear Operators ◽  
Well Posedness ◽  
Multiplier Theorems ◽  
Degenerate Differential Equations ◽  
Necessary And Sufficient ◽  
Closed Linear Operators

Abstract We study the well-posedness of the fractional degenerate differential equation: Dα (Mu)(t) + cDβ(Mu)(t) = Au(t) + f(t), (0 ≤ t ≤ 2π) on Lebesgue-Bochner spaces Lp(𝕋; X) and periodic Besov spaces $\begin{array}{} B_{p,q}^s \end{array}$ (𝕋; X), where A and M are closed linear operators in a complex Banach space X satisfying D(A) ⊂ D(M), c ∈ ℂ and 0 < β < α are fixed. Using known operator-valued Fourier multiplier theorems, we give necessary and sufficient conditions for Lp-well-posedness and $\begin{array}{} B_{p,q}^s \end{array}$-well-posedness of above equation.

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.

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