相关论文: Tail spaces estimates on Hamming cube and Bernstei…
For a certain class of algebras $\cal A$ we give a method for constructing Banach spaces $X$ such that every operator on $X$ is close to an operator in $\cal A$. This is used to produce spaces with a small amount of structure. We present…
We present unified approach to obtain sharp mean-squared and multiplicative inequalities of Hardy-Littlewood-Poly\'a and Taikov types for multiple closed operators acting on Hilbert space. We apply our results to establish new sharp…
This is a companion paper to our previous one, Avatars of Stein's Theorem in the complex setting. In this previous paper, we gave a sufficient condition for an integrable function in the upper-half plane to have an integrable Bergman…
We point out analogies between (a) the explicit formulas in analytic number theory and transversal index theory, (b) Lichtenbaum's recent conjectures on special values of Hasse-Weil zeta functions and a formula for special values of Ruelle…
We describe the eigenvalues and the eigenspaces of the adjacency matrices of subgraphs of the Hamming cube induced by Hamming balls, and more generally, by a union of adjacent concentric Hamming spheres. As a corollary, we extend the range…
We introduce the concept of an $E$-valued function algebra, a type of Banach algebra that consist of continuous $E$-valued functions on some compact Hausdorff space, where $E$ is a Banach algebra. We present some basic results about such…
We give a domination condition implying good-$\lambda$ and exponential inequalities for couples of measurable functions. Those inequalities recover several classical and new estimations involving some operators in Harminic Analysis. Among…
For bounded linear operators $A,B$ on a Hilbert space $\mathcal{H}$ we show the validity of the estimate $$ \sum_{\lambda \in \sigma_d (B)} \dist(\lambda, \overline{\num}(A))^p \leq \| B-A \|_{\mathcal{S}_p}^p$$ and apply it to recover and…
In this paper, the weighted estimates for multilinear pseudo-differential operators were systematically studied in rearrangement invariant Banach and quasi-Banach spaces. These spaces contain the Lebesgue space, the classical Lorentz space…
We establish the Krylov--Safonov theory for a large class of nonlocal operators of order $2s \in (0,2)$ on hyperbolic spaces $\mathbb{H}^{n}_{\kappa}$ with curvature $-\kappa<0$. We prove the Alexandrov--Bakelman--Pucci (ABP) estimates,…
The aim of this paper is investigating of Orlicz spaces with exponential function and correspondence Orlicz norm: we introduce some new equivalent norms, obtain the tail characterization, study the product of functions in Orlicz spaces etc.…
In this paper we study sharp pointwise inequalities for maximal operators. In particular, we strengthen DeVore's inequality for the moduli of smoothness and a logarithmic variant of Bennett--DeVore--Sharpley's inequality for rearrangements.…
Motivated by applications to probability and mathematical finance, we consider a parabolic partial differential equation on a half-space whose coefficients are suitably Holder continuous and allowed to grow linearly in the spatial variable…
Let $A, B$ and $X$ be $n\times n$ matrices such that $A, B$ are positive semidefinite. We present some refinements of the matrix Cauchy-Schwarz inequality by using some integration techniques and various refinements of the Hermite--Hadamard…
This paper investigates the asymptotics of the number of prime values taken by a polynomial in several variables with integer coefficients. Based on probabilistic heuristics and the multidimensional Bateman Horn conjecture, the expected…
In several applications, ultimately at the largest data, truncation effects can be observed when analysing tail characteristics of statistical distributions. In some cases truncation effects are forecasted through physical models such as…
New proofs of the classical Hermite-Hadamard inequality are presented and several applications are given, including Hadamard-type inequalities for the functions, whose derivatives have inflection points or whose derivatives are convex.…
We develop a functional calculus for $d$-tuples of non-commuting elements in a Banach algebra. The functions we apply are free analytic functions, that is nc functions that are bounded on certain polynomial polyhedra.
The notion of retro Banach frame with the help of b-linear functional in n-Banach spaces is being presented. Some properties related to the construction of new retro Banach frame in n-Banach space have been studied. In n-Banach spaces, some…
We study best approximations in Banach spaces via Birkhoff-James orthogonality of functionals. To exhibit the usefulness of Birkhoff-James orthogonality techniques in the study of best approximation problems, some algorithms and distance…