Weighted norm estimates and maximal regularity

By Sönke Blunck, P. Kunstmann. Advances in Differential Equations, 2002

54 citations recorded by the source corpus.

We give a sufficient condition for maximal regularity of the evolution equation u′(t) − Au(t) = f(t), t ≥ 0, u(0) = 0, in Lp-spaces. Our condition is a weighted norm estimate for the semigroup (e) and it is strictly weaker than the assumption that the e are integral operators whose kernels satisfy Gaussian estimates. As an application we present new results for the maximal regularity of Schrödinger operators with singular potentials, elliptic higher order operators with bounded measurable coefficients, and elliptic second order operators with singular lower order terms. Moreover, we prove a similar result for maximal regularity of the discrete time evolution equation un+1 − Tun = fn, n ∈ N0, u0 = 0.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/82ad13c59efa3869ed2e62e5dc0f065e7c207853

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In Applied Mathematics

1. P. Auscher
2. Frédéric Bernicot
3. Jiman Zhao
4. J. M. Martell
5. S. Hofmann
6. D. Cruz-Uribe
7. Andrei K. Lerner
8. A. Mcintosh

In Mathematical Physics

1. Frédéric Bernicot
2. Jiman Zhao
3. J. M. Martell
4. P. Auscher
5. S. Hofmann
6. A. Axelsson
7. T. Coulhon
8. Lixin Yan

Citations in the corpus

• New Abstract Hardy Spaces (2007, result): “r T and T∗ whose hypotheses are satisfied thanks to Theorem 8.8, 8.9 and 8.6. Then we conclude by duality for p ≥ 2. ⊓⊔ Remark 8.11 We recall the result of S. Blunck and P.C. Kunstmann (Theorem 1.1 of [9]). Assume that the semigroup etL satisfies for p 0 < 2 < q0 the following Lp0 −Lq0 off-diagon”
• Riesz Transforms of Schrödinger Operators on Manifolds (2012, unknown): “Since the semigroup is bounded analytic on L for p ∈ (p1, p1) we can apply [7] Theorem 1.”
• Weighted norm inequalities, off-diagonal estimates and elliptic operators. Part III: Harmonic analysis of elliptic operators (2006, methodology): “(w) that we established in Theorem 4.2. However, we wish to give a different proof using extrapolation and preceding ideas. Note that 2 may not be contained in IntJw(L) and the interpolation method of [BK2] may not work here. 32 PASCAL AUSCHER AND JOSE MAR´ ´IA MARTELL Proof. There are three steps. F”
• Weighted norm inequalities, off-diagonal estimates and elliptic operators Part II: Off-diagonal estimates on spaces of homogeneous type (2006, unknown): “See their series of papers [BK1, BK2, BK3].”