On operator-valued Fourier multipliers

By Shangquan Bu. 2006

98 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/77c9c4a3908019831baffbed429ffec66aa5a87a

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In Applied Mathematics

Citations in the corpus

Strong solutions for a compressible fluid model of Korteweg type (2008, unknown): “[1,6,15]) the data u0 and ρ0 necessarily satisfy u0 ∈ B2−2/p pp (Ω;Rn), ρ0 ∈ B3−2/p pp (Ω).”
Sobolev, Besov and Triebel-Lizorkin spaces on quantum tori (2015, background): “Note that the theory of vectorvalued Sobolev spaces is well-known and can be found in many books on the subject (see, for instance, [2]).”
Traces and embeddings of anisotropic function spaces (2012, unknown): “(ii) An extensive treatment of operator-valued Fourier multipliers on Besov spaces can be found in [4, 21, 26].”
Maximal regularity with temporal weights for parabolic problems with inhomogeneous boundary conditions (2012, background): “We refer to [2], [19] or [24] for a definition and the properties of these spaces.”
Interpolation, embeddings and traces of anisotropic fractional Sobolev spaces with temporal weights (2012, background): “For the definitions and properties of these spaces we refer to [3], [28] or [33].”
Stochastic integration in quasi-Banach spaces (2006, background): “We recall some basic definitions and results below, and refer to [3, 67, 79, 85] for more details on vector-valued Besov spaces defined via this approach (these references ‘only’ deal with the Banach-space parameter range, i.”
Anisotropic function spaces and maximal regularity for parabolic problems Part 1: Function spaces (2009, background): “2 in [5] to anisotropic Banach spaces.”
Sharp embedding results for spaces of smooth functions with power weights (2011, background): “Also vector-valued function spaces are intensively studied (see [2, 3, 36, 37, 38, 43, 45] and references therein).”
Fourier embeddings and Mihlin‐type multiplier theorems (2004, unknown): “1 Suppose ∥∥δdα h f∥∥t ≤ 2μ(n/t−Γ|α|)hαΓ for all |α|∞ ≤ 1, where d ∈ Z+, t ∈ [1, 2] is a Fouriertype for the underlying space X , q ∈ [1, t′] with q <∞, and Γ > 1/t− 1/q′.”
lp ‐maximal regularity for fractional difference equations on UMD spaces (2015, methodology): “For instance, on the real line, it has been treated by means of the Amann-Weiss multiplier theorem [4], [42] and on compact intervals by use of the Arendt-Bu multiplier theorem [6], [7].”
Periodic solutions of degenerate differential equations in vector-valued function spaces (2011, background): “Contrary to the L case, the multiplier theorems established so far are valid for arbitrary Banach spaces; see [1], [4] and [20].”