Operator–valued Fourier multiplier theorems on Besov spaces

By Maria Girardi, Lutz Weis. 2003

133 citations recorded by the source corpus.

Subfields: Applied Mathematics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/438216d47101f6aebb93b2e47eb8342ae3d101ad

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

1. Carlos Lizama
2. Tuomas Hytönen
3. V. Keyantuo
4. Mark Veraar
5. Ferenc Weisz
6. Rodrigo Ponce
7. Lutz Weis
8. Hans G. Feichtinger

In Statistics and Probability

1. Richard Nickl
2. Tuomas Hytönen
3. Ferenc Weisz
4. Hans G. Feichtinger
5. Markus Reiß
6. Carlos Lizama
7. V. Keyantuo
8. Mark Veraar

Citations in the corpus

• Maximal regularity for a class of integro-differential equations with infinite delay in Banach spaces (2005, methodology): “For results about operator-valued Fourier multipliers and R-boundedness (which we use in the next section), we refer to Amann [1], Bourgain [7], Clément–de Pagter–Sukochev–Witvliet [12], Weis [31, 32], Girardi–Weis [18], [19], Clément–Da Prato [11] and Arendt–Bu [5].”
• Operator-valued Fourier multiplier theorems on Lp(X) and geometry of Banach spaces (2003, background): “1”
• Traces and embeddings of anisotropic function spaces (2012, background): “emark 5.3. (i) In the scalar case Fourier multiplier results of the above type can be found in [49]. (ii) An extensive treatment of operator-valued Fourier multipliers on Besov spaces can be found in [4, 21, 26]. (iii) Thecondition onmguaranteesthat mfˆandhenceTmfisawell-definedelement ofS′(Rd;X) for”
• The Segal Algebra ${\bf S}_0({\Bbb R}^d)$ and Norm Summability of Fourier Series and Fourier Transforms (2006, result): “(i) was proved in Girardi and Weis [11] and (ii) in Okoudjou [20].”
• 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].”
• Summability of Multi-Dimensional Trigonometric Fourier Series (2012, result): “(i) was proved in Girardi andWeis [42] and (ii) in Okoudjou [67].”
• A Donsker Theorem for Lévy Measures (2012, methodology): “(c) The Fourier multiplier property of m follows from the Mihlin multiplier theorem for Besov spaces (see e.g. Triebel (2010) and particularly the scalar version of Cor. 4.11(b) in Girardi and Weis (2003)): because of (b) the function m is bounded and satisfies |um′(u)| .”
• Fourier embeddings and Mihlin‐type multiplier theorems (2004, methodology): “) With operator-norm estimates in place of strong ones, and these estimates required for all |α|1 ≤ n/t + 1 (instead of just those with also satisfy |α|∞ ≤ 1), this result is shown in Girardi and Weis [7] (Cor.”