Mikhlin's Theorem for Operator–Valued Fourier Multipliers in n Variables
By R. Haller, Horst Heck, A. Noll. 2002
75 citations recorded by the source corpus.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/6a2229696b367bf4d674eaa873ea075c41f8cfed
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In Applied Mathematics
- Mark Veraar
- J. V. Neerven
- Lutz Weis
- Robert Denk
- Matthias Hieber
- Ravi P. Agarwal
- Jan Prüss
- Martin J. Bohner
In Mathematical Physics
- Mark Veraar
- J. V. Neerven
- Robert Denk
- Lutz Weis
- Jan Prüss
- Matthias Hieber
- Veli B. Shakhmurov
- Alberto Venni
Citations in the corpus
- New thoughts on old results of R.T. Seeley (2004, background): “in n dimensions (see [Wei01], [SW00], [ HHN01 ] or Theorem 3.25 of [DHP01]) implies that, for |α |= 2m, the operators D α A −1 0 are bounded in X = Lp(R n ; E), as well as in H s p (R n ; E) for each s ∈ R. Hence the first condition of the perturbation theorem 3.2 holds provided the L∞-norms of a 1 ”
- Optimal Lp-Lq-estimates for parabolic boundary value problems with inhomogeneous data (2007, background): “For vector-valued Fourier multiplier theorems in several variables, see also [ 22 ], [34], [12 ]a nd [29].”
- Embedding operators and maximal regular differential-operator equations in Banach-valued function spaces (2005, background): “On the other hand, in vector-valued function spaces, Fourier multipliers have been studied, for example, by [3, 6, 12, 15, 20, 21, 29].”
- Operator-valued Fourier multiplier theorems on Lp(X) and geometry of Banach spaces (2003, unknown): “1”
- Stochastic Integration in Banach Spaces - a Survey (2013, background): “As a consequence, UMD spaces provide a natural framework for vector-valued harmonic analysis, and indeed large parts of the theory of singular integrals have by now been extended to UMD spaces [6, 40, 42, 45, 69, 98, 101].”
- Anisotropic function spaces and maximal regularity for parabolic problems Part 1: Function spaces (2009, unknown): “Noll [37].”
- Linear and nonlinear nonlocal boundary value problems for differential-operator equations (2006, background): “2 If E is a UMD space and n1⁄4 1 or if E is a UMD space with property ( ) [6] and n>1, then E satisfies the multiplier condition (see also [5,11]).”