Results 11 to 20 of about 1,114,131 (237)

Identification of Fully Measurable Grand Lebesgue Spaces [PDF]

Journal of Function Spaces, 2017
We consider the Banach function spaces, called fully measurable grand Lebesgue spaces, associated with the function norm ρ(f)=ess supx∈X⁡δ(x)ρp(x)(f), where ρp(x) denotes the norm of the Lebesgue space of exponent p(x), and p(·) and δ(·) are measurable ...
Giuseppina Anatriello, Ralph Chill, Alberto Fiorenza   +2 more
doaj   +2 more sources

Lipschitz Spaces and Mixed Lebesgue Spaces [PDF]

Proceedings of the American Mathematical Society, 1982
It is shown that translation invariant linear operators which improve Lipschitz classes behave almost as well as the corresponding fractional Riesz transforms when applied to the mixed Lebesgue spaces. These results partially generalize some of the theorems concerning Riesz transforms and mixed Lebesgue classes due to Adams and Bagby, Lizorkin, and ...
W. R. Madych
openaire   +3 more sources

$$\theta$$-Lebesgue spaces [PDF]

Journal of Mathematical Sciences
Traditional Lp spaces are fundamental in functional analysis, demarcated by the relationship $1/p + 1/q = 1$. This research pioneers the concept of $\theta$-Lebesgue space, stemming from a simultaneous weakening of both the classical $L_p$ relation and its $\theta$-variant, $1/(\theta(p)) + 1/(\theta(q)) = 1$.
Choudhury, Shouvik Datta
core   +5 more sources

Hermite-Hadamard's Inequality and the p-HH-Norm on the Cartesian Product of Two Copies of a Normed Space [PDF]

, 2008
The Cartesian product of two copies of a normed space is naturally equipped with the well-known p-norm. In this paper, another notion of norm is introduced, and will be called the p-HH-norm. This norm is an extension of the generalised logarithmic mean
Dragomir, Sever S, Kikianty, Eder
core   +6 more sources

Well-posedness of generalized magnetohydrodynamic equations in variable Lebesgue spaces [PDF]

Electronic Journal of Differential Equations
This article concerns the well-posedness of the generalized magnetohydrodynamic equations in variable Lebesgue spaces. By using some basic properties of variable Lebesgue spaces and decay estimates of the fractional heat kernel, we prove the existence ...
Jinyi Sun, Yuanwei Mai, Minghua Yang
doaj   +2 more sources

On the Lebesgue and Sobolev spaces on a time-scale [PDF]

Opuscula Mathematica, 2019
We consider the generalized Lebesgue and Sobolev spaces on a bounded time-scale. We study the standard properties of these spaces and compare them to the classical known results for the Lebesgue and Sobolev spaces on a bounded interval.
Ewa Skrzypek, Katarzyna Szymańska-Dębowska   +1 more
doaj   +1 more source

Lebesgue Points of Besov and Triebel–Lizorkin Spaces with Generalized Smoothness

Mathematics, 2021
In this article, the authors study the Lebesgue point of functions from Hajłasz–Sobolev, Besov, and Triebel–Lizorkin spaces with generalized smoothness on doubling metric measure spaces and prove that the exceptional sets of their Lebesgue points have ...
Ziwei Li, Dachun Yang, Wen Yuan
doaj   +1 more source

Bilinear multipliers of weighted Lebesgue spaces and variable exponent Lebesgue spaces [PDF]

Journal of Inequalities and Applications, 2013
The authors consider bilinear multipliers of the form \[ (f,g) \mapsto \int \limits _{\mathbb{R}^{n}} \int \limits _{\mathbb{R}^{n}} \widehat{f}(\xi)\widehat{g}(\eta)m(\xi,\eta)\exp(2i\pi \langle \cdot, \xi+\eta \rangle)d\xi d\eta, \] acting on weighted or variable exponent \(L^p\) spaces (here \(m\in L^{\infty}(\mathbb{R}^{2n};\mathbb{C})\)).
Kulak, Oznur, Gurkanli, A. Turan
openaire   +3 more sources

Boundedness of Commutators of Marcinkiewicz Integrals on Nonhomogeneous Metric Measure Spaces

Journal of Function Spaces, 2015
Let (X,d,μ) be a metric measure space satisfying the upper doubling condition and geometrically doubling condition in the sense of Hytönen. The aim of this paper is to establish the boundedness of commutator Mb generated by the Marcinkiewicz integral M ...
Guanghui Lu, Shuangping Tao
doaj   +1 more source

On Boundedness of Fractional Hadamard Integration and Hadamard-Type Integration in LebesgueSpaces with Mixed Norm

Современная математика: Фундаментальные направления, 2022
In this paper, we consider the boundedness of integrals of fractional Hadamard integration and Hadamard-type integration (mixed and directional) in Lebesgue spaces with mixed norm.
M. U. Yakhshiboyev
doaj   +1 more source