Related papers: The class $B_\infty$

The goal of this paper is to extend Nakai's generalized Morrey spaces to a wider function class, the one-sided Muckenhoupt weighted case. Morrey matching Muckenhoupt enables us to study the weak and strong type boundedness of one-sided…

We give two weighted norm estimates for higher order commutator of classical operators such as singular integral and fractional type operators, between weighted $L^p$ and certain spaces that include Lipschitz, BMO and Morrey spaces. We also…

Takahasi and Hatori introduced a class of commutative Banach algebras which satisfy a Bochner-Schoenberg-Eberlein-type inequality. Baised on their results we introduced a class of commutative Fr\'echet algebras which satisfy this property.…

We prove that the weighted quasi-Banach algebras of operator valued matrices satisfying Schur and Baskakov-Gohberg-Sj\"ostrand (BGS) conditions are inverse-closed in the Banach algebra $B(\ell^2(X,\mathcal{H}))$ whenever the weight is…

In this paper our aim is to deduce some complete monotonicity properties and functional inequalities for the Bickley function. The key tools in our proofs are the classical integral inequalities, like Chebyshev, H\"older-Rogers,…

In this paper we extend some previous results on weak pseudo-bosons and on their related bi-coherent states. The role of {\em compatible} functions is discussed in details, and some examples are considered. The pseudo-bosonic ladder…

We study integrability properties of a general version of the Boltzmann collision operator for hard and soft potentials in $n$-dimensions. A reformulation of the collisional integrals allows us to write the weak form of the collision…

We first study subextensions of m-subharmonic functions in weighted energy classes with given boundary values. The results are used to approximate an m-subharmonic function in weighted energy classes with given boundary values by an…

For any $p\in[1,\infty)$, we prove that the set of simple functions taking at most $k$ different values is proximinal in B\"ochner spaces $L^p(X)$ whenever $X$ is a dual Banach space with $w^*$-sequentially compact unit ball. With…

Sukochev and Zanin resolved an open problem due to B. Simon concerning optimal constants in H\"older inequality for the weak Schatten classes of compact operators. In this note we observe that these constants, by introducing the modified…

We show that the non pluripolar product of positive currents is a bimeromorphic invariant. Under some natural assumptions, we show that the (weighted) energy associated to big cohomology classes are also bimeromorphic invariants. We compare…

In this note we study sub-Hardy Hilbert spaces on which the the action of the operator of multiplication by the coordinate function z is assumed to be weaker than that of an isometry. We identify such operators with a class of weighted…

We give a classification between weighted norm inequalities of strong fractional integral operators, and their associated multi-parameter Muckenhoupt characteristics, bu considering the weights to be power functions. As a result, we extend…

Let $X$ be a metric space equipped with a metric $d$ and a nonnegative Borel measure $\mu$ satisfying the doubling property and let $\{\mathcal{A}_t\}_{t>0}$, be a generalized approximations to the identity, for example $\{\mathcal{A}_t\}$…

We consider the pointwise weighted approximation by Bernstein operators with inner singularities. The related weight functions are weights $\bar{w}(x)=|x-\xi|^\alpha(0<\xi<1,\ \alpha>0).$ In this paper we give direct and inverse results of…

We prove that for a Banach algebra $A$ having a bounded $\mathcal{Z}(A)$-approximate identity and for every $\bf[IN]$ group $G$ with weight $w$ which is either constant on conjugacy classes or $w \geq 1$, $\mathcal{Z}\big(L^1_w(G)…

Bennett, DeVore and Sharpley introduced the space weak $L^{\infty}$ in 1981 and studied its relationship with functions of bounded mean oscillation. Here we characterize weak $L^{\infty}$ in measure spaces without using the decreasing…

In the paper we continue the research of Bors\'{i}k and Dobo\v{s} on functions which allow us to introduce a metric to the product of metric spaces. In this paper we extend their scope on broader class of spaces which usually fail to…

Given a complete Riemannian manifold satisfying a weighted Poincar\'{e} inequality and having a bounded below Ricci curvature, various vanishing theorems for harmonic functions and harmonic 1-forms have been published. We generalized these…

In this article, we examine an approximate version of Koldobsky-Blanco-Turn\v{s}ek theorem (namely, Property P) in the space of vector-valued integrable functions. More precisely, we prove that the Lebesgue-Bochner spaces…