Related papers: Addendum to "Maximal regularity and Hardy spaces"
In this work, we consider the Cauchy problem for $u' - Au = f$ with $A$ the Laplacian operator on some Riemannian manifolds or a sublapacian on some Lie groups or some second order elliptic operators on a domain. We show the boundedness of…
There are some inaccuracies and errors in my article "Dual and almost-dual homogeneous spaces". Here I will describe in detail how to correct incorrect statements from this article and which statements there will have to be reformulated in…
We make corrections on the paper by Sugino [{\it JHEP} {\bf 0501} (2005) 016].
We correct here two errors in our earlier paper "An algebraic model for finite loop spaces" [arXiv:1212.2033]
We present several regularity results for a biological network formulation model originally introduced by D. Cai and D. Hu in {\it Phys. Rev. Lett.}, {\bf 111}(2013), 138701. A consequence of these result is that a stationary weak solution…
The preliminary material of the monograph (arXiv:1607.03852) written by the first two authors contains two major imprecisions that necessitates a number of (in the end harmless) changes throughout the entire text. One is about…
In this note we improve the parameter $q$ that appears in Theorem 1 obtained by the author in [Math. Ineq. \& appl., Vol 19 (3) (2016), 1013-1030].
We investigate the problem of $L^p$-maximal regularity on Banach spaces having a Schauder basis. Our results improve those of a recent paper.
A revised version of the last appendix of the (previous) paper "Existence and Regularity for an Energy Maximization Problem in Two Dimensions" by S.Kamvissis and E.A.Rakhmanov, that appeared in the Journal of Mathematical Physics, v.46,…
We correct an error in [I. Kangasniemi, and J. Onninen, On the heterogeneous distortion inequality. Math. Ann. 384 (2022), no. 3-4, 1275-1308.]
The paper continues our previous work [7] on the radius of subregularity that was initiated by Asen Dontchev. We extend the results of [7] to general Banach/Asplund spaces and to other classes of perturbations, and sharpen the coderivative…
The Hardy-Rellich inequality in the whole space with the best constant was firstly proved by Tertikas and Zographopoulos in Adv. Math. (2007) in higher dimensions $N\geq 5$. Then it was extended to lower dimensions $N\in \{3, 4\}$ by…
There is a mathematical error in the first version of this paper. A new corrected version will be posted when the error is fixed, possibly with a modified title.
In this paper we prove maximal regularity estimates in "square function spaces" which are commonly used in harmonic analysis, spectral theory, and stochastic analysis. In particular, they lead to a new class of maximal regularity results…
We provide a precise statement and self contained proof of a Sobolev inequality (cf. [A, page 236 and page 237]) stated in the original paper. Higher order and fractional inequalities are treated as well.
This note points out a gap in the proof of the main theorem of the article "Birationally rigid hypersurfaces" published in Invent. Math. 192 (2013), 533-566, and provides a new proof of the theorem.
Building on the author's recent work with Jan Maas and Jan van Neerven, this paper establishes the equivalence of two norms (one using a maximal function, the other a square function) used to define a Hardy space on $\R^{n}$ with the…
Some mathematical errors of the paper commented upon [W.-M. Suen, Phys. Rev. D 40, (1989) 315] are corrected.
Lemma 4.8 in the article [Regularity structures and renormalisation of FitzHugh-Nagumo SPDEs in three space dimensions, Electronic J. Probability 21 (18):1-48 (2016), arXiv:1504.02953] contains a mistake, which implies a weaker regularity…
Let (M, g) be a complete Riemannian manifold. Assume that the Ricci curvature of M has quadratic decay and that the volume growth is strictly faster than quadratic. We establish that the Hardy spaces of exact 1-differential forms on M ,…