Related papers: Cpmposed Grand Lebesgue Spaces

We characterize strong continuity of general operator semigroups on some Lebesgue spaces. In particular, a characterization of strong continuity of weighted composition semigroups on classical Hardy spaces and weighted Bergman spaces with…

In this paper, we show that the interpolation spaces between Grand, small or classical Lebesgue are so called Lorentz-Zygmund spaces or more generally $G\Gamma$-spaces. As a direct consequence of our results any Lorentz-Zygmund space…

We extend the classical Lebesgue-Riesz norm estimations for integral operators acting between different classical Lebesgue-Riesz spaces into the Grand Lebesgue Spaces, in the general case. As an example we consider matrix operators acting…

{\it We study the class of all rearrangement-invariant (=r.i.) function spaces $E$ on $[0,1]$ such that there exists $0<q<1$ for which $ \Vert \sum_{_{k=1}}^n\xi_k\Vert_{E}\leq Cn^{q}$, where $\{\xi_k\}_{k\ge 1}\subset E$ is an arbitrary…

Aiming to generalize the well-trained gaze estimation model to new target domains, Cross-domain Gaze Estimation (CDGE) is developed for real-world application scenarios. Existing CDGE methods typically extract the domain-invariant features…

In this article, we introduce a class of multilinear strongly singular integral operators with generalized kernels on the RD-space. The boundedness of these operators on weighted Lebesgue spaces is established. Moreover, two types of…

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 article, we study the space of subgroups of generalized Baumslag-Solitar groups (GBS groups), that is, groups acting cocompactly on an oriented tree without inversion and with infinite cyclic vertex and edge stabilizers. Our results…

Motivated by a seminal paper of professor M. Z. Nashed published in 1987 on classification of ill-posed linear operator equations and distinguishing two types of ill-posedness in Banach and Hilbert spaces, we present, illustrate and justify…

The classical Gagliardo-Nirenberg interpolation inequality is a well-known estimate which gives, in particular, an estimate for the Lebesgue norm of intermediate derivatives of functions in Sobolev spaces. We present an extension of this…

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…

In this paper we begin the study of some important Banach spaces of slice hyperholomorphic functions, namely the Bloch, Besov and weighted Bergman spaces, and we also consider the Dirichlet space, which is a Hilbert space. The importance of…

L^p spaces of mappings taking values in arbitrary metric spaces, which we call nonlinear Lebesgue spaces, play an important role in several fields of mathematics. For instance, membership in these spaces is typically required for transport…

Let $G$ be a locally compact group which is $\sigma $-compact, endowed with a left Haar measure $\lambda .$ Denote by $e$ the unit element of $G$, and by $B$ an open relatively compact and symmetric neighbourhood of $e$. For every $(p,q) $…

In this article we investigate the Fourier series and transforms for the functions defined on the [-pi, pi]^ d or on the R^d and belonging to the (Bilateral) Grand Lebesgue Spaces. As a particular case we obtain some results about Fourier's…

All continuous translation invariant complex-valued valuations on Lebesgue measurable functions are completely classified. And all continuous rotation invariant complex-valued valuations on spherical Lebesgue measurable functions are also…

Given $E_0, E_1, E, F$ rearrangement invariant spaces, $a, b, b_0, b_1$ slowly varying functions and $0\leq \theta_0<\theta_1\leq 1$, we characterize the interpolation space $$(\overline{X}_{\theta_0,b_0,E_0}, \overline{X}^{\mathcal…

Let $G$ be a locally compact group and also let $H$ be a compact subgroup of $G$. It is shown that, if $\mu$ is a relatively invariant measure on $G/H$ then there is a well-defined convolution on $L^1(G/H,\mu)$ such that the Banach space…

This is the second part in a series dealing with subspaces of de Branges spaces of entire function generated by majorization on subsets of the closed upper half-plane. In this part we investigate certain Banach spaces generated by…

Let $\Bc$ denote the real-valued functions continuous on the extended real line and vanishing at $-\infty$. Let $\Br$ denote the functions that are left continuous, have a right limit at each point and vanish at $-\infty$. Define $\acn$ to…