Related papers: A Christ-Kiselev maximal theorem in quasi-Banach f…

In this paper we completely characterize the norm attainment set of a bounded linear operator on a Hilbert space. This partially answers a question raised recently in [\textit{D. Sain, On the norm attainment set of a bounded linear…

In this paper, we provide a unifying theory concerning the convergence properties of the so-called max-product Kantorovich sampling operators based upon generalized kernels in the setting of Orlicz spaces. The approximation of functions…

In a prior work [Hilbert transform along smooth families of lines math.CA/0310345] the authors introduced a variant of the Kakeya maximal function associated with Lipschitz maps from the plane into the unit circle. In this paper, we improve…

We prove sufficient conditions for the boundedness of the maximal operator on variable Lebesgue spaces with weights $\varphi_{t,\gamma}(\tau)=|(\tau-t)^\gamma|$, where $\gamma$ is a complex number, over arbitrary Carleson curves. If the…

Let $\alpha\in{\Bbb R}$, $0<p<\infty$ and $X$ be a ball quasi-Banach function space on ${\Bbb R}^n$. In this article, we introduce the Herz-type space $\dot{K}^{\alpha,p}_X({\Bbb R}^n)$ associated with $X$. We identify the dual space of…

In this paper, we consider the structure of maximally monotone operators in Banach space whose domains have nonempty interior and we present new and explicit structure formulas for such operators. Along the way, we provide new proofs of the…

We derive in this preprint the exact up to multiplicative constant non-asymptotical estimates for the norms of some non-linear in general case operators, for example, the so-called maximal functional operators, in two probabilistic…

Properties of first-order Sobolev-type spaces on abstract metric measure spaces, so-called Newtonian spaces, based on quasi-Banach function lattices are investigated. The set of all weak upper gradients of a Newtonian function is of…

We show that lattice isomorphisms between lattices of slowly oscillating functions on chain-connected proper metric spaces induce coarsely equivalent homeomorphisms. This result leads to a Banach-Stone-like theorem for these lattices.…

We show that there exist infinite-dimensional extremely non-complex Banach spaces, i.e. spaces $X$ such that the norm equality $\|Id + T^2\|=1 + \|T^2\|$ holds for every bounded linear operator $T:X\longrightarrow X$. This answers in the…

Let $X$ be a ball quasi-Banach function space on ${\mathbb R}^n$. In this article, the authors introduce the weak Hardy-type space $WH_X({\mathbb R}^n)$, associated with $X$, via the radial maximal function. Assuming that the powered…

In this paper, we develop a thorough analysis of the boundedness properties of the maximal operator for the Bochner-Riesz means related to the Fourier-Bessel expansions. For this operator, we study weighted and unweighted inequalities in…

We study extreme contractions in the setting of finite-dimensional polyhedral Banach spaces. Motivated by the famous Krein-Milman Theorem, we prove that a \emph{rank one} norm one linear operator between such spaces can be expressed as a…

Suppose $X$ is a locally solid vector lattice. It is known that there are several non-equivalent notions for compact operators on $X$. Furthermore, notion of the $AM$-property in $X$ as an extension for the $AM$-spaces in Banach lattices…

Let $A,$ $T$ and $B$ be bounded linear operators on a Banach space. This paper is concerned mainly with finding some necessary and sufficient conditions for convergence in operator norm of the sequences $\left\{ A^{n}TB^{n}\right\} $ and…

Let $X$ be a ball quasi-Banach function space on ${\mathbb R}^n$. In this article, assuming that the powered Hardy--Littlewood maximal operator satisfies some Fefferman--Stein vector-valued maximal inequality on $X$ as well as it is bounded…

In this paper, we survey recent progress on the theory of maximally monotone operators in general Banach space. We also extend various of the results and leave some open questions.

The classical Kantorovich-Rubinstein duality theorem establishes a significant connection between Monge optimal transport and maximization of a linear form on the set of 1-Lipschitz functions. This result has been widely used in various…

We prove a Cayley-Bacharach-type theorem for points in projective space $\mathbb{P}^n$ that lie on a complete intersection of $n$ hypersurfaces. This is made possible by new bounds on the growth of the Hilbert function of almost complete…

Let $\mathcal{E}(X,d,\mu)$ be a Banach function space over a space of homogeneous type $(X,d,\mu)$. We show that if the Hardy-Littlewood maximal operator $M$ is bounded on the space $\mathcal{E}(X,d,\mu)$, then its boundedness on the…