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1
Content available remote On certain nonlinear integral operators
100%
Misiak A. , Ryż A.
Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
|
2001
|
tom [Z] 41
135-142
2
Content available remote Closedness of the set of extreme points in Orlicz spaces with Orlicz norm
100%
Wisła M.
Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
|
2001
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tom [Z] 41
221-240
EN
In this paper the problem of closedness of the set of exreme points of the unit ball of Orlicz spaces equipped with Orlicz norm over a non-negative, atomless, [ro]-finite and complete measure space in discussed.
3
Content available remote On a converse inequality for maximal functions in Orlicz spaces
100%
Kita H.
Studia Mathematica
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1996
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tom 118
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nr 1
1-10
EN
Let $Φ(t) = ʃ_{0}^{t} a(s)ds$ and $Ψ(t) = ʃ_{0}^{t} b(s)ds$, where a(s) is a positive continuous function such that $ʃ_{1}^{∞} a(s)/s ds = ∞$ and b(s) is quasi-increasing and $lim_{s→∞}b(s) = ∞$. Then the following statements for the Hardy-Littlewood maximal function Mf(x) are equivalent: (j) there exist positive constants $c_1$ and $s_{0}$ such that $ʃ_{1}^{s} a(t)/t dt ≥ c_{1}b(c_{1}s)$ for all $s ≥ s_{0}$; (jj) there exist positive constants $c_2$ and $c_3$ such that $ʃ_{0}^{2π} Ψ((c_2)/(|⨍|_{𝕋}) |⨍(x)|) dx ≤ c_3 + c_{3} ʃ_{0}^{2π} Φ(1/(|⨍|_{𝕋})) Mf(x) dx$ for all $⨍ ∈ L^{1}(𝕋)$.
4
Content available remote Topological properties of spaces of linear operators on non-locally convex Orlicz spaces
80%
Oelke A.
Commentationes Mathematicae
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2010
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tom Vol. 50, [Z] 2
103-108
EN
We study the topological properties of the space L(L^Φ,X) of all continuous linear operators from an Orlicz space L^Φ (an Orlicz function Φ is not necessarily convex) to a Banach space X.We provide the space L(L^Φ,X) with the Banach space structure. Moreover, we examine the space Ls(L^Φ,X) of all singular operators from L^Φ to X.
5
Content available remote Modular function spaces and control functions of almost everywhere convergence
80%
Kita H. , Miyamoto T. , Yoneda K.
Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
|
2001
|
tom [Z] 41
99-133
EN
The modular spaces have been studied by many authors. In this paper we consider the modular function spaces which provide a generalization of Banach function spaces, and discuss some relations between properties of these spaces and control functions of almost everywhrere convergence of functions in modular function spaces. We give a necessary and sufficient condition for a control function to be in the same modular function space as functions appearing in almost everywhere convergence.
6
Content available remote The Riesz angle of Orlicz function spaces
80%
Jincai W.
Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
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2000
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tom [Z] 40
209-223
EN
By using a new quantitative index of N-function, we estimate and calculate the Riesz angle of Orlicz function spaces equipped with either Luxemburg norm or Orlicz norm.
7
Content available remote Compact midpoint local uniform convexity in Orlicz spaces
80%
Li X. , Cui Y.
Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
|
2002
|
tom [Z] 42(1)
53-62
EN
In this paper, we introduce a new geometric property in Banach spaces, namely compact midpoint local uniform convexity. Criteria for this property in Orlicz spaces are given for both norms in the function case as well as in the sequence case.
8
Content available remote On a pair of geometric parameters of Orlicz norm
80%
Yan Y.
Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
|
2001
|
tom [Z] 41
257-263
9
Content available remote On theorem of Grothendieck type
80%
Narloch A.
Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
|
2001
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tom [Z] 41
143-146
10
Content available remote On nonlinear integral equations in some functions spaces
80%
Bardaro C. , Musielak J. , Vinti G.
Demonstratio Mathematica
|
2002
|
tom Vol. 35, nr 3
583-592
EN
There are established some conditions for existence of solutions of a nonlinear integral equation Tf =f+g, where T is a convolution-type integral operator.
11
Content available remote Summing multi-norms defined by Orlicz spaces and symmetric sequence space
80%
Blasco O.
Commentationes Mathematicae
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2016
|
tom Vol 56, No. 1
145--168
EN
We develop the notion of the (X1,X2)-summing power-norm based on a~Banach space E, where X1 and X2 are symmetric sequence spaces. We study the particular case when X1 and X2 are Orlicz spaces ℓΦ and ℓΨ respectively and analyze under which conditions the (Φ,Ψ)-summing power-norm becomes a~multinorm. In the case when E is also a~symmetric sequence space L, we compute the precise value of ∥(δ1,⋯,δn)∥n(X1,X2), where (δk) stands for the canonical basis of L, extending known results for the (p,q)-summing power-norm based on the space ℓr which corresponds to X1=ℓp, X2=ℓq, and E=ℓr.
12
Content available Summing multi-norms defined by Orlicz spaces and symmetric sequence space
80%
Blasco O.
Commentationes Mathematicae
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2016
|
tom 56
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nr 1
EN
We develop the notion of the \((X_1,X_2)\)-summing power-norm based on a~Banach space \(E\), where \(X_1\) and \(X_2\) are symmetric sequence spaces. We study the particular case when \(X_1\) and \(X_2\) are Orlicz spaces \(\ell_\Phi\) and \(\ell_\Psi\) respectively and analyze under which conditions the \((\Phi, \Psi)\)-summing power-norm becomes a~multinorm. In the case when \(E\) is also a~symmetric sequence space \(L\), we compute the precise value of \(\|(\delta_1,\cdots,\delta_n)\|_n^{(X_1,X_2)}\) where \((\delta_k)\) stands for the canonical basis of \(L\), extending known results for the \((p,q)\)-summing power-norm based on the space \(\ell_r\) which corresponds to \(X_1=\ell_p\), \(X_2=\ell_q\), and \(E=\ell_r\).
13
Content available remote Integral of function with values in complete modular space
80%
Liskowski M.
Demonstratio Mathematica
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2002
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tom Vol. 35, nr 2
347-356
EN
The theorem on existence of an integral of a function with values in a modular space and some fundamental properties of this integral are given.
14
Content available The exact values of nonsquare constants for a class of Orlicz spaces
80%
Wang J.
Opuscula Mathematica
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2005
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tom Vol. 25, no. 2
325-332
EN
We extend the MDelta-condition from [10] and introduce the PhiDelta-condition at zero. Next we discuss nonsquare constant in Orlicz spaces generated by an N-function Phi(u) which satisfy PhiDelta-condition. We obtain exact value of nonsquare constant in this class of Orlicz spaces equipped with the Luxemburg norm.
15
Content available remote Boundedness of Toeplitz type operators associated to Riesz potential operator with general kernel on Orlicz space
70%
Chen D.
Open Mathematics
|
2015
|
tom 13
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nr 1
EN
In this paper, the boundedness properties for some Toeplitz type operators associated to the Riesz potential and general integral operators from Lebesgue spaces to Orlicz spaces are proved. The general integral operators include singular integral operator with general kernel, Littlewood-Paley operator, Marcinkiewicz operator and Bochner-Riesz operator.
16
Content available remote Continuity of the metric projection in Orlicz space
70%
Teng Y. , Wang T. , Li M.
Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
|
1999
|
tom [Z] 39
109-116
EN
Let (f(n)) be a sequence of functions converging in norm to f in some rotund Orlicz function or se-quence space endowed with the Luxemburg norm or the Orlicz norm, and let (C(n)) be a sequence of convex sets satisfying some condition and tending in suitable way to a ser C. Then the best norm approximation of f(n) with respect to C(n) converges in norm to the best approximation of f with respect to C.
17
Content available remote Partial integral operators in Orlicz spaces with mixed norm
70%
Appelli J. , Kalitvin A. S. , Zabreĭko P. P.
Colloquium Mathematicum
|
1998
|
tom 78
|
nr 2
293-306
18
Content available remote Approximation in Orlicz-Slobodeckii space by functions in C[infinity] (Omega)
60%
Liskowski M.
Fasciculi Mathematici
|
1999
|
tom Nr 29
43-59
EN
We wish to prove that [...] is dense in Orlicz-Slobodeckii space Bk.M (n) for some n c RN offinite measure.
19
Content available remote Modelling a solution of a homogeneous parabolic equation with random initial condition from Lp(Ω)
60%
Kuchinka K. , Slyvka-Tylyshchak G.
Przegląd Elektrotechniczny
|
2023
|
tom R. 99, nr 5
77--82
EN
In this paper, a model of solutions to the heat equation with initial conditions from the Orlicz space Lp(Ω) of random variables is built. The constructed model approximates the solution of a homogeneous parabolic equation with given reliability and accuracy in some Orlicz space.
PL
W pracy zbudowano model rozwiązan równania ciepła z warunkami początkowymi z przestrzeni Orlicza Lp(Ω) zmiennych losowych. Skonstruowany model przybliza rozwiązanie jednorodnego równania parabolicznego z zadaną niezawodnoscią i dokładnoscią w pewnej przestrzeni Orlicza.
20
Content available remote On (∆2) condition in density-type topologies
60%
Filipczak M. , Terepeta M.
Demonstratio Mathematica
|
2011
|
tom Vol. 44, nr 2
423--432
EN
We discuss properties of density-type topologies Tψ connected with condition (∆2) similar to the condition considered in the theory of Orlicz spaces. Density-type topologies Tψ introduced in [5] may not be invariant under multiplication by a number. This property is strictly connected with the condition, which we call (∆2), by analogy with well known condition introduced in Orlicz spaces. Like in the theory of Orlicz spaces, (∆2) condition causes that the considered topologies are more convenient for examination and have simpler properties. Moreover, the power functions are also of great importance as a handy instrument. Recall some basic facts. Let (Ω, Σ, μ) be a measure space and A be a family of all functions φ: [0, ∞) → [0, ∞) which are continuous, nondecreasing, such that φ(0) = 0, φ(x) > 0 for x > 0 and limx→∞ φ(x) = ∞.
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