Results 21 to 30 of about 56,469 (146)

A direct approach to the duality of grand and small Lebesgue spaces [PDF]

Nonlinear Analysis: Theory, Methods & Applications, 2009
Let \(\mathcal{M}_{0}\) be the set of all Lebesgue measurable function in the interval \((0,1)\), finite a.e.\ in it and let \(\mathcal{M}_{0}^{+}\) be the class of all nonnegative functions of \(\mathcal{M}_{0}\). For \(f \in \mathcal{M}_{0}\), the decreasing rearrangement \(f^{*}\) of \(f\) is defined by \[ f^{*} = \inf\{ \lambda > 0: |\{x \in (0,1):
G. DI FRATTA, FIORENZA, ALBERTO
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Hardy type inequality in variable Lebesgue spaces [PDF]

, 2008
We prove that in variable exponent spaces $L^{p(\cdot)}(\Omega)$, where $p(\cdot)$ satisfies the log-condition and $\Omega$ is a bounded domain in $\mathbf R^n$ with the property that $\mathbf R^n \backslash \bar{\Omega}$ has the cone property, the ...
Rafeiro, Humberto, Samko, Stefan
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Cyclicity in families of circle maps [PDF]

, 2013
In this paper we will study families of circle maps of the form x↦x+2πr+af(x)(mod2π) and investigate how many periodic trajectories maps from this family can have for a ‘typical’ function f provided the parameter a is ...
Arnol’d, Benyamini, Christensen, O. KOZLOVSKI, Preiss   +4 more
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Lebesgue points via the Poincar\'e inequality [PDF]

, 2014
In this article, we show that in a $Q$-doubling space $(X,d,\mu),$ $Q>1,$ which satisfies a chain condition, if we have a $Q$-Poincar\'e inequality for a pair of functions $(u,g)$ where $g\in L^Q(X),$ then $u$ has Lebesgue points $H^h$-a.e.
Karak, Nijjwal, Koskela, Pekka
core   +1 more source

Hölder Quasicontinuity in Variable Exponent Sobolev Spaces

Journal of Inequalities and Applications, 2007
We show that a function in the variable exponent Sobolev spaces coincides with a Hölder continuous Sobolev function outside a small exceptional set.
Katja Tuhkanen, Juha Kinnunen, Petteri Harjulehto   +2 more
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Bilateral Small Lebesgue Spaces

, 2009
19 ...
Ostrovsky, Eugene, Sirota, Leonid
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Solutions of an anisotropic nonlocal problem involving variable exponent

Advances in Nonlinear Analysis, 2013
The present paper deals with an anisotropic Kirchhoff problem under homogeneous Dirichlet boundary conditions, set in a bounded smooth domain of ℝN ().
Avci Mustafa, Ayazoglu (Mashiyev) Rabil A., Cekic Bilal   +2 more
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Combined effects for non-autonomous singular biharmonic problems

, 2020
We study the existence of nontrivial weak solutions for a class of generalized $p(x)$-biharmonic equations with singular nonlinearity and Navier boundary condition. The proofs combine variational and topological arguments.
Repovš, Dušan D., Rădulescu, Vicenţiu D.   +1 more
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Analyticity and Existence of the Keller–Segel–Navier–Stokes Equations in Critical Besov Spaces

Advanced Nonlinear Studies, 2018
This paper deals with the Cauchy problem to the Keller–Segel model coupled with the incompressible 3-D Navier–Stokes equations. Based on so-called Gevrey regularity estimates, which are motivated by the works of Foias and Temam [20], we prove that the ...
Yang Minghua, Fu Zunwei, Liu Suying
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The Boundedness of Generalized Fractional Integral Operators on Small Morrey Spaces

Cauchy: Jurnal Matematika Murni dan Aplikasi
The small Morrey space is the set of locally Lebesgue integrable functions with norm defined supremum over radius of ball . This paper aims to prove the boundedness properties of the generality of fractional integral operators in small Morrey spaces ...
Rizky Aziz Syaifudin, Corina Karim, Marjono Marjono, Hairur Rahman   +3 more
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