共查询到20条相似文献,搜索用时 15 毫秒
1.
Positivity - For a monotone Orlicz function $$\varPhi $$ taking only values 0 and $$\infty $$ , it is showed that in both cases, the s-homogeneous norm $$\Vert \cdot \Vert _{\varPhi ,s}$$ , if... 相似文献
2.
Positivity - A new characterization of the exponential type Orlicz spaces generated by the functions $$\exp (|x|^p)-1$$ ( $$p\ge 1$$ ) is given. We define norms for centered random variables... 相似文献
3.
Luboš Pick 《Georgian Mathematical Journal》1994,1(1):77-97
The aim of the present paper is to characterize the classes of weights which ensure the validity of one-weighted strong, weak, or extra-weak type estimates in Orlicz classes for the integral operator $$H_0 f(x) = \frac{2}{\pi }\int_0^\infty {\frac{{yf(y)}}{{x^2 - y^2 }}dy, x \in (0,\infty )}$$ . 相似文献
4.
Journal of Fourier Analysis and Applications - Given an ergodic dynamical system $$(X, \mathcal {B}, \mu , T)$$, we prove that for each function f belonging to the Orlicz space $$L(\log L)^2(\log... 相似文献
5.
Mathematical Notes - A characterization of disjointly homogeneous Orlicz–Lorentz function spaces $$\Lambda_{\varphi,w}$$ is obtained. It is used to find necessary and sufficient conditions... 相似文献
6.
Fengping Yao 《Archiv der Mathematik》2017,108(1):85-97
In this paper we give a new alternative proof of the local higher integrability in Orlicz spaces of the gradient for weak solutions of quasilinear parabolic equations of p-Laplacian typefor any p > 0. Moreover, we point out that our results are homogeneousregularity estimates in Orlicz spaces and improve the known results for such equations by using some new techniques. Actually, our results can be extended to the global estimates and cover a more general class of degenerate/singular parabolic problems of p-Laplacian type.
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$$\begin{array}{ll} u_t-\text{div} \left( \left | \nabla u\right|^{ p-2 } \nablau\right)=\text{div} \left(| \mathrm{ \bf f}|^{p-2} \mathrm{ \bf f}\right)\quad {\rm in}~\Omega\times (0,T] \end{array}$$
7.
In this note, we introduce the concepts of weak finitely regular relations and weak hypercontinuous posets. It is proved that when a binary relation $$\rho :X/\rightarrow Y$$ satisfies a certain condition, $$\rho $$ is weak finitely regular if and only if $$(\varphi _{\rho }(X,Y),\subseteq )$$ is a weak hypercontinuous poset. For a poset P, we get that the relation $$\not \le $$ on P is weak finitely regular if and only if P is weak hypercontinuous. 相似文献
8.
Yan Yaqiang 《Southeast Asian Bulletin of Mathematics》2002,25(4):769-782
We introduce some practical calculation of the weakly convergent sequence coefficients of Orlicz sequence spaces equipped with Luxemburg norm and Orlicz norm. For the N-function (u) of which the index function is monotonuous, the exact value WCS(l()) of Orlicz sequence space l() with Luxemburg norm is available, i.e. WCS(l()) =
or
WCS(l) of l with Orlicz norm has the exact value
or estimation
相似文献
9.
Archiv der Mathematik - We give some regularity criterion (of a weak $$-L^{p}$$ Serrin type) of a weak solution to the 3D Navier–Stokes equations in a bounded domain $$\Omega \subset \mathbb... 相似文献
10.
We give necessary and sufficient conditions for the boundedness of generalized fractional integral and maximal operators on Orlicz–Morrey and weak Orlicz–Morrey spaces. To do this, we prove the weak–weak type modular inequality of the Hardy–Littlewood maximal operator with respect to the Young function. Orlicz–Morrey spaces contain spaces (), Orlicz spaces, and generalized Morrey spaces as special cases. Hence, we get necessary and sufficient conditions on these function spaces as corollaries. 相似文献
11.
Positivity - The result of the title is: an archimedean $$\ell $$ -group with weak unit A is (isomorphic to) $$C(\mathcal {L})$$ for some (identifiable) locale $$\mathcal {L}$$ (or, $$\mathbb... 相似文献
12.
D. V. Salekhov 《Mathematical Notes》1968,3(2):92-99
For functions in Orlicz space L
M
*
, we study the behavior of
(t)dt, where x* (t) is non-increasing and equimeasurable with ¦ x(t) ¦. We establish the existence of unbounded functions in L
M
*
that are not limits of bounded functions and for which
. Moreover, we establish a new criterion for an N-function to belong to the class 2 and a sufficiency test for a function to belong to Orlicz space.Translated from Matematicheskie Zametki, Vol. 3, No. 2, pp. 145–156, February, 1968. 相似文献
13.
Robert ?erny 《NoDEA : Nonlinear Differential Equations and Applications》2012,19(5):575-608
We give a version of the Moser–Trudinger inequality for Orlicz–Sobolev spaces embedded into exponential and multiple exponential spaces on unbounded domains in ${\mathbb R^n, n \geq 2}$ . Applying this result and the Mountain Pass Theorem we study the existence of non-trivial weak solutions to the problem $$\begin{array}{ll}u \in W^1 L^{\Phi}(\mathbb R^n)\quad{\rm and}\\\quad -{\rm div} \left(\Phi ' (|\nabla u|)\frac{\nabla u}{|\nabla u|}\right)+V(x)\Phi'(|u|)\frac{u}{|u|} =f(x,u)\quad{\rm in}\, \mathbb R^n,\end{array}$$ where Φ is a Young function such that the space ${W^1 L^{\Phi}(\mathbb R^n)}$ is embedded into an Orlicz space of the exponential or multiple exponential type, the nonlinearity f(x, t) has the corresponding critical growth and V(x) is a continuous potential. 相似文献
14.
Journal of Theoretical Probability - Two hypotheses on the class $${\mathcal {L}}(\gamma )$$ in the class $$\mathcal {OS}\cap \mathcal {ID}$$ are discussed. Two weak hypotheses on the class... 相似文献
15.
If
is an RUC-basis in somecouple of non-commutative L
p-spaces, then
is an RUC-basic sequence in any non-commutative Orlicz or Lorentz space which is an interpolation space for this couple. 相似文献
16.
We study the regularity properties of local minimizers of non-autonomous convex integral functionals of the type when the integrand f has almost linear growth with respect to the gradient variable and the dependence on the x-variable is controlled by a function which belongs to a suitable Orlicz Sobolev space.
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$$\begin{aligned} \mathcal {F}( u, \Omega )= \int _{\Omega } \! f(x,Du) \, \,dx, \end{aligned}$$
17.
The Ramanujan Journal - We construct bases of the space of harmonic weak Maass forms of weight $$\kappa \in \frac{1}{2}{\mathbb {Z}}$$ . Using these bases, we obtain a Shintani lift from a positive... 相似文献
18.
Positivity - This paper is devoted to the study of efficient elements for set-valued maps. We propose two new notions of relative weak $$\epsilon $$ -efficient element and strict relative weak... 相似文献
19.
Let X be a compact convex set and let ext X stand for the set of extreme points of X. We show that if $$f:X\rightarrow {\mathbb {R}}$$ is an affine function with the point of continuity property such that $$f\le 0$$ on $${\text {ext}}\,X$$, then $$f\le 0$$ on X. As a corollary of this minimum principle, we obtain a generalization of a theorem by C.H. Chu and H.B. Cohen by proving the following result. Let X, Y be compact convex sets such that every extreme point of X and Y is a weak peak point and let $$T:\mathfrak {A}^c(X)\rightarrow \mathfrak {A}^c(Y)$$ be an isomorphism such that $$\left\| T\right\| \cdot \left\| T^{-1}\right\| <2$$. Then $${\text {ext}}\,X$$ is homeomorphic to $${\text {ext}}\,Y$$. 相似文献
20.
The weak tightness wt(X) of a space X was introduced in Carlson (Topol Appl 249:103–111, 2018) with the property $$wt(X)\le t(X)$$. We investigate several well-known results concerning t(X) and consider whether they extend to the weak tightness setting. First we give an example of a non-sequential compactum X such that $$wt(X)=\aleph _0<t(X)$$ under $$2^{\aleph _0}=2^{\aleph _1}$$. In particular, this demonstrates the celebrated Balogh’s (Proc Am Math Soc 105(3):755–764, 1989) Theorem does not hold in general if countably tight is replaced with weakly countably tight. Second, we introduce the notion of an S-free sequence and show that if X is a homogeneous compactum then $$|X|\le 2^{wt(X)\pi \chi (X)}$$. This refines a theorem of de la Vega (Topol Appl 153:2118–2123, 2006). In the case where the cardinal invariants involved are countable, this also represents a variation of a theorem of Juhász and van Mill (Proc Am Math Soc 146(1):429–437, 2018). In this connection we also show $$w(X)\le 2^{wt(X)}$$ for a homogeneous compactum. Third, we show that if X is a $$T_1$$ space, $$wt(X)\le \kappa $$, X is $$\kappa ^+$$-compact, and $$\psi (\overline{D},X)\le 2^\kappa $$ for any $$D\subseteq X$$ satisfying $$|D|\le 2^\kappa $$, then (a) $$d(X)\le 2^\kappa $$ and (b) X has at most $$2^\kappa $$-many $$G_\kappa $$-points. This is a variation of another theorem of Balogh (Topol Proc 27:9–14, 2003). Finally, we show that if X is a regular space, $$\kappa =L(X)wt(X)$$, and $$\lambda $$ is a caliber of X satisfying $$\kappa <\lambda \le \left( 2^{\kappa }\right) ^+$$, then $$d(X)\le 2^{\kappa }$$. This extends of theorem of Arhangel$$'$$skiĭ (Topol Appl 104:13–26, 2000). 相似文献