Related papers: Quasi Grand Lebesgue Spaces
A natural class of ideals, almost isometric ideals, of Banach spaces is defined and studied. The motivation for working with this class of subspaces is our observation that they inherit diameter 2 properties and the Daugavet property.…
In this paper structure of infinite dimensional Banach spaces is studied by using an asymptotic approach based on stabilization at infinity of finite dimensional subspaces which appear everywhere far away. This leads to notions of…
In this paper we first take a detail survey of the study of the Banach-Saks property of Banach spaces and then show the Banach-Saks property of the product spaces generated by a finite number of Banach spaces having the Banach-Saks…
We prove some results on weakly almost square Banach spaces and their relatives. On the one hand, we discuss weak almost squareness in the setting of Banach function spaces. More precisely, let $(\Omega,\Sigma)$ be a measurable space, let…
The theory of Banach spaces of Dirichlet series has drawn an increasing attention in the recent 25 years. One of the main interest of this new theory is that of defining analogues of the classical spaces of analytic functions on the unit…
In this paper we prove off-diagonal, limited range, multilinear, vector-valued, and two-weight versions of the Rubio de Francia extrapolation theorem in general quasi-Banach function spaces. We prove mapping properties of the generalization…
In this paper, we analyze multi-dimensional quasi-asymptotically $c$-almost periodic functions and their Stepanov generalizations as well as multi-dimensional Weyl $c$-almost periodic type functions. We also analyze several important…
We give a new proof of a characterization of the closeness of the range of a continuous linear operator and of the closeness of the sum of two closed vector subspaces of a Banach space. Then we state sufficient conditions for the closeness…
We deduce continuity, compactness and invariance properties for quasi-Banach Orlicz modulation spaces. We characterize such spaces in terms of Gabor expansions and by their images under the Bargmann transform.
In a series of previous papers, we initiated a systematic study of semihypergroups and had a thorough discussion on certain analytic and algebraic aspects associated to this class of objects. In particular, we introduced the notion of…
We introduce a new class of Banach spaces, called generalized-lush spaces (GL-spaces for short), which contains almost-CL-spaces, separable lush spaces (specially, separable $C$-rich subspaces of $C(K)$), and even the two-dimensional space…
We develop a general, functional calculus approach to approximation of $C_0$-semigroups on Banach spaces by bounded completely monotone functions of their generators. The approach comprises most of well-known approximation formulas, yields…
We extend the classical Hardy-Sobolev-Poincare-Wirtinger inequalities from the ordinary Lebesgue-Riesz spaces into the Grand Lebesgue ones, with exact constants evaluation.
In this paper, we continue our study of quasihyperbolic metric in Banach spaces. The main results of the paper present a criterion for smoothness of geodesics of quasihyperbolic type metrics in Banach spaces, under a Dini type condition on…
The main aim of this paper is to introduce and analyze the notions of subspace almost periodicity and subspace weak almost periodicity for $C$-distribution semigroups and $C$-distribution cosine functions in Banach spaces. We continue our…
Density of Lipschitz functions in Newtonian spaces based on quasi-Banach function lattices is discussed. Newtonian spaces are first-order Sobolev-type spaces on abstract metric measure spaces defined via (weak) upper gradients. Our main…
In the paper under review, we introduce the notions of various types of generalized (asymptotical) almost periodicity with variable exponents. We define and thoroughly analyze an important subclass of (asymptotically) Stepanov almost…
In this article we investigate an action of some operators (not necessary to be linear or sublinear) in the so-called (Bilateral) Grand Lebesgue Spaces (GLS), in particular, double weight Fourier operators, maximal operators, imbedding…
The concept of angle, angle functions, and the question how to measure angles present old and well-established mathematical topics referring to Euclidean space, and there exist also various extensions to non-Euclidean spaces of different…
We deduce an extension theorem for the so-called Sobolev-Grand Lebesgue Spaces defined on the suitable subsets of the whole finite-dimensional Euclidean space, and estimate the norms of correspondent extension operator, which may be choosed…