Related papers: Continuous maximal regularity in locally convex sp…
If X is a sequentially complete locally convex space, then a quotient bounded operator T is regular (in the sense of Waelbroeck) if and only if it is a bounded element (in the sense of Allan) of the algebra of quotient bounded operators on…
In this paper we collect several examples of convergence of functions of random processes to generalized functionals of those processes. We remark that the limit is always finitely absolutely continuous with respect to Wiener measure. We…
The minimax theory for estimating linear functionals is extended to the case of a finite union of convex parameter spaces. Upper and lower bounds for the minimax risk can still be described in terms of a modulus of continuity. However in…
We study the relations between some geometric properties of maximal monotone operators and generic geometric and analytical properties of the functions on the associate Fitzpatrick family of convex representations. We also investigate under…
In this note, we extend the regularity theory for monotone measure-preserving maps, also known as optimal transports for the quadratic cost optimal transport problem, to the case when the support of the target measure is an arbitrary convex…
The optimization problem concerning the determination of the minimizer for the sum of convex functions holds significant importance in the realm of distributed and decentralized optimization. In scenarios where full knowledge of the…
We introduce the class of $\alpha$-firmly nonexpansive and quasi $\alpha$-firmly nonexpansive operators on $r$-uniformly convex Banach spaces. This extends the existing notion from Hilbert spaces, where $\alpha$-firmly nonexpansive…
The paper is devoted to a systematic study and characterizations of notions of local maximal monotonicity and their strong counterparts for set-valued operators that appear in variational analysis, optimization, and their applications. We…
This paper develops a novel approach to necessary optimality conditions for constrained variational problems defined in generally incomplete subspaces of absolutely continuous functions. Our approach involves reducing a variational problem…
We continue the investigation into the computational status of the existence of moduli of regularity (and their use for rates of convergence) in the sense of Kohlenbach, Lopez and Nicolae (2019), carried out w.r.t. classical reverse…
In this paper, we define for the first time the local Morrey-type space associated with ball quasi-Banach function spaces and show the related series of properties. In addition, Hardy-Littlewood maximal operator's boundedness is proved. We…
The purpose of this article is to study Lipschitz CR mappings from an $h$-extendible (or semi-regular) hypersurface in $\mbb C^n$. Under various assumptions on the target hypersurface, it is shown that such mappings must be smooth. A…
This is a survey on recent progress concerning maximal regularity of non-autonomous equations governed by time-dependent forms on a Hilbert space. It also contains two new results showing the limits of the theory.
In this paper we introduce the class of infinite infimal convolution functionals and apply these functionals to the regularization of ill-posed inverse problems. The proposed regularization involves an infimal convolution of a continuously…
We study the Hardy-Littlewood maximal operator defined via an unconditional norm, acting on block decreasing functions. We show that the uncentered maximal operator maps block decreasing functions of special bounded variation to functions…
In this work we are concerned with maximality of monotone operators representable by certain convex functions in non-reflexive Banach spaces. We also prove that these maximal monotone operators satisfy a Bronsted-Rockafellar type property.…
Szemer\'edi's regularity lemma is a fundamental tool in extremal graph theory, theoretical computer science and combinatorial number theory. Lov\'asz and Szegedy [L. Lov\'asz and B. Szegedy: Szemer\'edi's Lemma for the analyst, Geometric…
We obtain a strengthening of the principle of local reflexivity in a general form. The added strength makes local reflexivity operators respect given subspaces. Applications are given to bounded approximation properties of pairs, consisting…
We prove the local Lipschitz regularity of the minimizers of functionals of the form \[ \mathcal I(u)=\int_\Omega f(\nabla u(x))+g(x)u(x)\,dx\qquad u\in\phi+W^{1,1}_0(\Omega) \] where $g$ is bounded and $\phi$ satisfies the Lower Bounded…
We prove some regularity results for a priori bounded local minimizers of non-autonomous integral functionals of the form $$\mathcal{F}(v,\Omega)=\int_\Omega F(x,Dv)dx,$$ under the constraint $v \ge \psi$ a.e. in $\Omega$, where $\psi$ is a…