Operator–valued Fourier multiplier theorems and maximal $L_p$-regularity

By Lutz Weis. 2001

763 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/799181d9e3e159f7961eeb73756428280d640664

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In Applied Mathematics

1. Carlos Lizama
2. Mark Veraar
3. J. V. Neerven
4. V. Keyantuo
5. Tuomas Hytönen
6. Lutz Weis
7. Rodrigo Ponce
8. Roland Schnaubelt

In Mathematical Physics

1. Carlos Lizama
2. J. V. Neerven
3. V. Keyantuo
4. Mark Veraar
5. Tuomas Hytönen
6. Roland Schnaubelt
7. Lutz Weis
8. Robert Denk

Citations in the corpus

• Fourier multipliers and periodic solutions of delay equations in Banach spaces (2006, background): “Recently, a signiflcant progress has been made in flnding su‐cient conditions for operator valued functions to be Lp- Fourier multipliers, see [3], [ 21 ], the monograph”
• H^\infty functional calculus and square function estimates for Ritt operators (2012, background): “R-boundedness and R-Ritt operators This section starts with some background on R-boundedness, a notion which -by nowplays a prominent role in many questions concerning functional calculi, see in particular [29, 30, 60].”
• A structurally damped plate equation with Dirichlet-Neumann boundary conditions (2015, methodology): “It was shown by Weis in [31] that a sectorial operator in a Banach space of class HT has maximal Lq-regularity for all q ∈ (1,∞) if and only if the set {λ(λ+A)−1 : Reλ ≥ 0, λ 6= 0} is R-bounded.”
• Operator-valued Fourier multiplier theorems on Lp(X) and geometry of Banach spaces (2003, background): “…have had many applications in the theory of evolutions equations, in particular in connection with: maximal regularity of parabolic equations [4, 7, 11, 23, 37, 38], stability theory [17, 26, 36], elliptic operators on infinite dimensional state spaces [3], and pseudo differential operators on…”
• Littlewood-Paley-Stein theory for semigroups in UMD spaces (2007, background): “[4, 5, 13, 22]) suggests that the right side of (1.”
• Maximal Regularity for Nonautonomous Evolution Equations (2004, neutral): “In particular, Weis (see [22], [23]) characterized those operators on UMD spaces which possess maximal regularity in terms of R-boundedness.”
• Fractional evolution equations in Banach spaces (2001, methodology): “This is possible applying the following very recent generalization of the Michlin multiplier theorem due to Weis [72], Cl ement and Pr uss [22].”
• New Abstract Hardy Spaces (2007, background): “ Lp(Y) is equivalent to the fact that T is bounded on Lp(J × Y). That is why we study this operator. Of course, the problem of maximal Lq regularity is completely understood by the abstract result in [32]. Here we want to remain as concrete as possible. In particular case we will see that the H1 ǫ,m”
• Periodic solutions of second order differential equations in Banach spaces (2006, methodology): “Since large classes of classical operators are R-bounded (cf. Girardi-Weis [24] and the recent memoir of Denk, Hieber and Prüss [16]), the assumptions in this approach are not too restrictive for applications.”