Results 21 to 30 of about 118,444 (224)

On small Lebesgue spaces

Journal of Function Spaces and Applications, 2005
We consider a generalized version of the small Lebesgue spaces, introduced in [5] as the associate spaces of the grand Lebesgue spaces. We find a simplified expression for the norm, prove relevant properties, compute the fundamental function and discuss ...
Claudia Capone, Alberto Fiorenza
doaj   +1 more source

Estimates for iterated commutators of multilinear square fucntions with Dini-type kernels

Journal of Inequalities and Applications, 2018
Let TΠb→ $T_{\Pi\vec {b}}$ be the commutator generated by a multilinear square function and Lipschitz functions with kernel satisfying Dini-type condition.
Zengyan Si, Qingying Xue
doaj   +1 more source

Weakly symmetric functions on spaces of Lebesgue integrable functions

Karpatsʹkì Matematičnì Publìkacìï, 2022
In this work, we present the notion of a weakly symmetric function. We show that the subset of all weakly symmetric elements of an arbitrary vector space of functions is a vector space.
T.V. Vasylyshyn, V.A. Zahorodniuk
doaj   +1 more source

Identification of Fully Measurable Grand Lebesgue Spaces

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   +1 more source

Generalized Grand Lebesgue Spaces Associated to Banach Function spaces [PDF]

Sahand Communications in Mathematical Analysis
In this paper we introduce the class of grand Lebesgue spaces associated to a Banach function space $X$ by replacing the role of the $L^1$-norm by the norm $\|\cdot\|_X$ in the classical construction of the generalized grand Lebesgue spaces.
Alireza Bagheri Salec, Seyyed Mohammad Tabatabaie, Alaa Mahdi Talib Albeka   +2 more
doaj   +1 more source

Decompositions of Nakano norms by ODE techniques

, 2018
We study decompositions of Nakano type varying exponent Lebesgue norms and spaces. These function spaces are represented here in a natural way as tractable varying $\ell^p$ sums of projection bands. The main results involve embedding the varying Lebesgue
Talponen, Jarno
core   +1 more source

Variable Lebesgue norm estimates for BMO functions [PDF]

Czechoslovak Mathematical Journal, 2012
Let \(f\in L^1_{\text{loc}}(\mathbb R^n)\), \(Q\) be a cube in \(\mathbb R^n\) and \(| Q| \) be the Lebesgue measure of \(Q\). Then \(f_Q=| Q| ^{-1}\int _Qf(t)\,dt\) and \(\| f\| _{\text{BMO}}=\sup \limits _Q| f-f_Q| _Q\). If \(\| f\| _{\text{BMO}}
Izuki, Mitsuo, Sawano, Yoshihiro
openaire   +2 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

Lebesgue Measurable Function In Fractional Differential Equations

Journal of Kufa for Mathematics and Computer, 2011
Bassam, M.A. [1], proved some existence and uniqueness theorems for the following fractional linear differential equation.
Sabah Mahmood Shaker
doaj   +1 more source

The Second Generalization of the Hausdorff Dimension Theorem for Random Fractals

Mathematics, 2022
In this paper, we present a second partial solution for the problem of cardinality calculation of the set of fractals for its subcategory of the random virtual ones.
Mohsen Soltanifar
doaj   +1 more source