On operator-valued Fourier multiplier theorems
By Željko Štrkalj, Lutz Weis. 2007
89 citations recorded by the source corpus.
The classical Fourier multiplier theorems of Marcinkiewicz and Mikhlin are extended to vector-valued functions and operator-valued multiplier functions on Z d or R d which satisfy certain R-boundedness conditions.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/651df22b40ada629924ead0a52dd4923d8239007
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
- Carlos Lizama
- Mark Veraar
- J. V. Neerven
- V. Keyantuo
- Lutz Weis
- Tuomas Hytönen
- Charles-Edouard Br'ehier
- Fabian Hornung
In Mathematical Physics
- Carlos Lizama
- J. V. Neerven
- Mark Veraar
- V. Keyantuo
- Lutz Weis
- Tuomas Hytönen
- Rico Zacher
- Robert Denk
Citations in the corpus
- Wiener amalgams and pointwise summability of Fourier transforms and Fourier series (2006, unknown): “The next theorem was proved in Herz [22], Peetre [29] and Girardi and Weis [17].”
- Maximal regularity for a class of integro-differential equations with infinite delay in Banach spaces (2005, methodology): “Versions of the multiplier theorems on the real line can be found in [2], [20], [21] (this reference contains criteria implying the R−boundedness property for operator families), [33] and [34].”
- 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): “Weis [64] and R.”
- Periodic solutions of second order differential equations in Banach spaces (2006, methodology): “In the non-periodic case, operator-valued Fourier multiplier theorems have been established by Amann [3], Weis [38], [39], Girardi-Weis [23], and Arendt-Batty-Bu [5].”