Related papers: Regular Maximal Monotone Multifunctions and Enlarg…
We obtain boundedness for the bilinear spherical maximal function in a range of exponents that includes the Banach triangle and a range of $L^p$ with $p<1$. We also obtain counterexamples that are asymptotically optimal with our positive…
In many applications such as web-based search, document summarization, facility location and other applications, the results are preferable to be both representative and diversified subsets of documents. The goal of this study is to select…
We study the norm derivatives in the context of Birkhoff-James orthogonality in real Banach spaces. As an application of this, we obtain a complete characterization of the left-symmetric points and the right-symmetric points in a real…
We present new sharp results concerning multipliers and distance estimates in various spaces of harmonic functions in the unit ball of $R^n$.
We prove strong convergence theorems of some iterative algorithms in a real uniformly smooth Banach space. The results presented extend, generalize and improve the corresponding results recently announced by many authors.
We study n-monotone functionals, which constitute a generalisation of n-monotone set functions. We investigate their relation to the concepts of exactness and natural extension, which generalise the notions of coherence and natural…
This paper introduces a new definition of $\alpha$-monotone operators in real 2-uniformly convex and smooth Banach spaces. Based on this new definition, we establish several novel structural and analytical properties of such operators,…
In this note we prove new coincidence results for multiple summing mappings, related to the cotypes of the Banach spaces involved.
We characterize the extreme points of multidimensional monotone functions from $[0,1]^n$ to $[0,1]$, as well as the extreme points of the set of one-dimensional marginals of these functions. These characterizations lead to new results for…
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…
An inequality, which combines the concept of completely monotone functions with the theory of divided differences, is proposed. It is a straightforward generalization of a result, recently introduced by two of the present authors.
In this paper we are concerned with the problem of local and global subextensions of (quasi-)plurisubharmonic functions from a "regular" subdomain of a compact K\"ahler manifold. We prove that a precise bound on the complex Monge-Amp\`ere…
In these notes, we present a general result concerning the Lipschitz regularity of a certain type of set-valued maps often found in constrained optimization and control problems. The class of multifunctions examined in this paper is…
In the present work, we discuss variational regularization for ill-posed nonlinear problems with focus on an oversmoothing penalty term. This means in our model that the searched-for solution of the considered nonlinear operator equation…
We characterize the solution of a broad class of convex optimization problems that address the reconstruction of a function from a finite number of linear measurements. The underlying hypothesis is that the solution is decomposable as a…
We study some sufficient conditions imposed on the sequence of martingale differences (m.d.) in the separable Banach spaces of continuous functions defined on the metric compact set for the Central Limit Theorem in this space. We taking…
We review various characterizations of uniform convexity and smoothness on norm balls in finite-dimensional spaces and connect results stemming from the geometry of Banach spaces with \textit{scaling inequalities} used in analysing the…
The aim of my thesis is to discuss, develop and apply the newest developments of this fascinating theory connected to modern harmonic analysis. In particular, we investigate some strong convergence result of partial sums of Vilenkin-Fourier…
Let $E$ be a uniformly smooth and uniformly convex real Banach space and $E^*$ be its dual space. Suppose $A : E\rightarrow E^*$ is bounded, strongly monotone and satisfies the range condition such that $A^{-1}(0)\neq \emptyset$. Inspired…
In this paper, we extend the investigations regarding Birkhoff-James orthogonality of linear operators to bounded continuous functions on metric spaces. We introduce Birkhoff-James extensions of continuous functions and study them in…