The operator-valued Marcinkiewicz multiplier theorem and maximal regularity

By Wolfgang Arendt, Shangquan Bu. 2002

251 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/90e01cdb268de4d4ef2a8ca18afaf9b341fd5ba3

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Citations in the corpus

A T1 theorem for integral transformations with operator-valued kernel (2006, background): “Pisier, written up in [1]: Proposition 1.”
Operator–valued Fourier multiplier theorems on Besov spaces (2003, background): “…in the theory of evolution equations, in particular, in connection with: maximal regularity of parabolic equations [2, 28, 27, 6, 18, 4], stability theory [29, 15, 20], elliptic operators on infinite dimensional state spaces [1], and pseudo differential operators on manifolds with…”
Fourier Multipliers and Integro‐Differential Equations in Banach Spaces (2004, methodology): “For more details, we refer to Arendt and Bu [3, 4].”
OPERATOR-VALUED FOURIER MULTIPLIERS ON PERIODIC BESOV SPACES AND APPLICATIONS (2004, methodology): “The following condition on sequences (Mk)k∈Z ⊂ L(X; Y ) was introduced in [3] to study Fourier multipliers in the L-context:”
Operator–valued Fourier Multipliers on Periodic Triebel Spaces (2005, background): “By Lemma 3.1 of [ 3 ], this implies that ˆ u(k) ∈ D(A )a ndikˆ u(k )= Aˆ u(k )+ x .T hus ( ik − A)ˆ u(k )= x. This shows that ik − A is surjective.”
Operator-valued Fourier multiplier theorems on Lp(X) and geometry of Banach spaces (2003, background): “…multiplier theorems 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…”
H^\infty functional calculus and square function estimates for Ritt operators (2012, background): “But if X is not isomorphic to a Hilbert space, then the unit ball of B(X) is not R-bounded (see [1]).”
Stochastic Integration in Banach Spaces - a Survey (2013, background): “Every R-bounded family is uniformly bounded; the converse holds if (and only if, see [1]) X has cotype 2 and Y has type 2.”
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].”
Maximal regularity for a class of integro-differential equations with infinite delay in Banach spaces (2005, methodology): “9 in various situations by use of the operator-valued multiplier theorems established in [5], [3], [6].”
Uniformly gamma-radonifying families of operators and and the stochastic Weiss conjecture (2006, methodology): “In a rephrasing in terms of sequential convergence in γ ( H, E ), this result is due to Neidhardt [39].”
Periodic solutions of degenerate differential equations in vector-valued function spaces (2011, methodology): “We also recall the following definition from [3].”
On operator-valued Fourier multipliers (2006, background): “case (see Theorem 1.3 in ref. [ 2 ] or Theorem 3 in ref.”
Maximal Lp-regularity for parabolic and elliptic equations on the line (2006, background): “to a Hilbert space, then R-boundedness is strictly stronger than boundedness (see [ AB02 ]).”
Fourier multipliers and periodic solutions of delay equations in Banach spaces (2006, methodology): “Recently, a significant progress has been made in finding sufficient conditions for operator valued functions to be L- Fourier multipliers, see [3], [21], the monograph [8] and literature therein.”
Periodic solutions of second order differential equations in Banach spaces (2006, methodology): “To achieve our goals, we make extensive use of recent results from the papers Arendt-Bu [6], [5] and Keyantuo-Lizama [25], and the methods are based on operatorvalued Fourier multipliers theorems.”