Wyniki wyszukiwania - Biblioteka Nauki

1

Best Constants for the Inequalities between Equivalent Norms in Orlicz Spaces

100%

Bang H. H. , Hoang N. V. , Huy V. N.

Bulletin of the Polish Academy of Sciences. Mathematics

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2011

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tom Vol. 59, no 2

165--174

EN

We investigate best constants for inequalities between the Orlicz norm and Luxemburg norm in Orlicz spaces.

2

On CLUR points of Orlicz spaces

63%

Wang Q. , Zhao L. , Wang T.

Annales Polonici Mathematici

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2000

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tom 73

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nr 2

147-157

EN

Criteria for compactly locally uniformly rotund points in Orlicz spaces are given.

3

Inégalités de Sobolev-Orlicz non-uniformes

51%

Carron G.

Colloquium Mathematicum

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1998

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tom 77

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nr 2

163-178

4

Weighted inequalities for one-sided maximal functions in Orlicz spaces

51%

Ortega Salvador P.

Studia Mathematica

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1998

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tom 131

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nr 2

101-114

EN

Let $M_{g}^{+}$ be the maximal operator defined by $M_{g}^{+}⨍(x) = sup_{h>0} (ʃ_{x}^{x+h} |⨍|g)/(ʃ_{x}^{x+h} g)$, where g is a positive locally integrable function on ℝ. Let Φ be an N-function such that both Φ and its complementary N-function satisfy $Δ_2$. We characterize the pairs of positive functions (u,ω) such that the weak type inequality $u({x ∈ ℝ | M_{g}^{+}⨍(x) > λ}) ≤ C/(Φ(λ)) ʃ_ℝ Φ(|⨍|)ω$ holds for every ⨍ in the Orlicz space $L_Φ(ω)$. We also characterize the positive functions ω such that the integral inequality $ʃ_ℝ Φ(|M_{g}^{+}⨍|)ω ≤ ʃ_ℝ Φ(|⨍|)ω$ holds for every $⨍ ∈ L_Φ(ω)$. Our results include some already obtained for functions in $L^p$ and yield as consequences one-dimensional theorems due to Gallardo and Kerman-Torchinsky.

5

Isomorphic Schauder decompositions in certain Banach spaces

51%

Marchenko V.

Open Mathematics

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2014

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tom 12

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nr 11

1714-1732

EN

We extend a theorem of Kato on similarity for sequences of projections in Hilbert spaces to the case of isomorphic Schauder decompositions in certain Banach spaces. To this end we use ℓψ-Hilbertian and ∞-Hilbertian Schauder decompositions instead of orthogonal Schauder decompositions, generalize the concept of an orthogonal Schauder decomposition to the case of Banach spaces and introduce the class of Banach spaces with Schauder-Orlicz decompositions. Furthermore, we generalize the notions of type, cotype, infratype and M-cotype of a Banach space and study the properties of unconditional Schauder decompositions in Banach spaces possessing certain geometric structure.

6

Henryk Hudzik : vita et opera

51%

Mastyło M. , Musielak J.

Commentationes Mathematicae

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2015

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tom Vol 55, No. 2

45--78

EN

This article contains a short vita of Henryk Hudzik's as well as a non-exhaustive survey of his contribution to various areas of analysis. We focus on the theory of Orlicz−Sobolev spaces and the geometry of Banach spaces. We highlight criteria for some important geometric properties related to the metric fixed point theory in some classes of Banach lattices, including Orlicz and Orlicz−Lorentz spaces, but we do not forget Henryk Hudzik's contribution to nonlinear integral equations and partial differential equations.

7

J-convexity constants

51%

Wang J.

Opuscula Mathematica

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2007

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tom Vol. 27, no. 1

167-174

EN

We introduce the J-convexity constants on Banach spaces and give some properties of the constants. We give the relations between the J-convexity constants and the n-th von Neumann-Jordan constants. Using the quantitative indices we estimate the value of J-convexity constants in Orlicz spaces.

8

Reverse-Holder classes in the Orlicz spaces setting

51%

Harboure E. , Salinas O. , Viviani B.

Studia Mathematica

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1998

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tom 130

|

nr 3

245-261

EN

In connection with the $A_ϕ $ classes of weights (see [K-T] and [B-K]), we study, in the context of Orlicz spaces, the corresponding reverse-Hölder classes $RH_ϕ$. We prove that when ϕ is $Δ_2$ and has lower index greater than one, the class $RH_ϕ$ coincides with some reverse-Hölder class $RH_q,q>1$. For more general ϕ we still get $RH_ϕ ⊂ A_∞ = ⋃_{q>1}RH_q$ although the intersection of all these $RH_ϕ$ gives a proper subset of $⋂_{q>1}RH_q$.

9

Topological properties of spaces of linear operators on non-locally convex Orlicz spaces

51%

Oelke A.

Commentationes Mathematicae

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2010

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tom 50

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nr 2

EN

We study the topological properties of the space $\mathcal{L}(L^\varphi, X)$ of all continuous linear operators from an Orlicz space $L^\varphi$ (an Orlicz function $\varphi$ is not necessarily convex) to a Banach space $X$. We provide the space $\mathcal{L}(L^\varphi ,X)$ with the Banach space structure. Moreover, we examine the space $\mathcal{L}_s (L^\varphi, X)$ of all singular operators from $L^\varphi$ to $X$.

10

Order of approximation for nonlinear sampling Kantorovich operators in Orlicz spaces

44%

Costarelli D. , Vinti G.

Commentationes Mathematicae

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2013

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tom Vol. 53, No. 2

171--192

EN

In this paper, we study the rate of approximation for the nonlinear sampling Kantorovich operators. We consider the case of uniformly continuous and bounded functions belonging to Lipschitz classes of the Zygmund-type, as well as the case of functions in Orlicz spaces. We estimate the aliasing errors with respect to the uniform norm and to the modular functional of the Orlicz spaces, respectively. The general setting of Orlicz spaces allows to deduce directly the results concerning the rate of convergence in Lp-spaces, 1 ≤ p < ∞, very useful in the applications to Signal Processing. Others examples of Orlicz spaces as interpolation spaces and exponential spaces are discussed and the particular cases of the nonlinear sampling Kantorovich series constructed using Fejér and B-spline kernels are also considered.

11

Generalized mixed topology on F-normed function spaces

44%

Kasior E. , Nowak M.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

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2004

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tom Vol. 44, nr 1

55--66

EN

Let (X, ||•||) be a F-normed function space over a σ-finite measure space (Ω, Σ, μ) and let ||•||0 denote the usual F-norm on L0 that generates the convergence in measure on subsets of finite measures. In X a natural two-normed convergence can be defined as follows: a sequence (xn) in X is said to be γ-convergent to x ϵ X whenever || xn - x||0 → 0 and supn||xn|| < ∞. In this paper we study locally solid topologies on X satisfying the continuity property with respect to this γ-convergence in X. We call such topologies "uniformly Lebesgue". These investigations are closely related to the theory of generalized inductive limit topologies in the sense of Turpin. In particular we show that a generalized mixed topology γT(Tφ, T0|Lφ) on the Orlicz space Lφ (φ is not assumed to be convex) is the finest uniformly Lebesgue topology on Lφ. Moreover, we characterize γφ-linear functionals on Lφ.

12

Note on the concentration-compactness principle for generalized Moser-Trudinger inequalities

38%

Černý R.

Open Mathematics

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2012

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tom 10

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nr 2

590-602

EN

Let Ω ⊂ ℝn, n ≥ 2, be a bounded domain and let α < n − 1. Motivated by Theorem I.6 and Remark I.18 of [Lions P.-L., The concentration-compactness principle in the calculus of variations. The limit case. I, Rev. Mat. Iberoamericana, 1985, 1(1), 145–201] and by the results of [Černý R., Cianchi A., Hencl S., Concentration-Compactness Principle for Moser-Trudinger inequalities: new results and proofs, Ann. Mat. Pura Appl. (in press), DOI: 10.1007/s10231-011-0220-3], we give a sharp estimate of the exponent concerning the Concentration-Compactness Principle for the embedding of the Orlicz-Sobolev space W 01 L n logα L(Ω) into the Orlicz space corresponding to a Young function that behaves like exp t n/(n−1−α) for large t. We also give the result for the case of the embedding into double and other multiple exponential spaces.

13

Uniformly $\mu$-Continuous Topologies on Orlicz-Bochner Spaces

38%

Feledziak K.

Commentationes Mathematicae

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2006

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tom 46

|

nr 1

EN

We examine the topological properties of Orlicz-Bochner spaces $L^\varphi(X)$ (over a σ-finite measure space $(\Omega, \Sigma, \mu))$, where $\varphi$ is an Orlicz function (not necessarily convex) and $X$ is a real Banach space. We continue the study of some class of locally convex topologies on $L^\varphi (X)$, called uniformly $\mu$-continuous topologies. In particular, the generalized mixed topology $\mathcal{T}_I^\varphi (X)$ on $L^\varphi (X)$ (in the sense of Turpin) is considered.

14

An inequality of Bohr and Favard for Orlicz spaces

38%

Bang H.

Bulletin of the Polish Academy of Sciences. Mathematics

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2001

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tom Vol. 49, no 4

381-387

EN

In this paper, we prove an inequality of Bohr and Favard for any Orlicz norm (with the same constants as in the Bohr-Favard inequality).

15

Double exponential integrability, Bessel potentials and embedding theorems

38%

Edmunds D. E. , Gurka P. , Opic B.

Studia Mathematica

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1995

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tom 115

|

nr 2

151-181

EN

This paper is a continuation of [5] and provides necessary and sufficient conditions for double exponential integrability of the Bessel potential of functions from suitable (generalized) Lorentz-Zygmund spaces. These results are used to establish embedding theorems for Bessel potential spaces which extend Trudinger's result.

16

Weak-sequential compactness on non-locally convex Orlicz spaces

32%

Nowak M.

Bulletin of the Polish Academy of Sciences. Mathematics

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1998

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tom Vol. 46, no 3

225-231

EN

Let [L^fi] be an Orlicz space defined by a finite valued Orlicz function [fi] (not necesarilly convex) over a [sigma]-finite atomless measure space. Let (L^fi[...] be the order continous dual of [L^fi]. It is proved that a subset Z of [L^fi] is conditionally sequentially sigma([L^fi],(L^fi])[...)-compact (i.e., every sequence in Z contains a sigma([L^[fi],(L^fi])[...])-Cauchy subsequence) if and only if Z is norm bounded in some Orlicz space [L^psi] where psi increases more rapidly than [...] (the convex minorant of fi).

17

Asymptotically isometric and isometric copies of ℓ1 in some Banach function lattices

32%

Kamińska A. , Mastyło M.

Commentationes Mathematicae

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2013

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tom Vol. 53, No. 2

283--300

EN

We identify the class of Calderón-Lozanovskii spaces that do not contain an asymptotically isometric copy of ℓ1, and consequently we obtain the corresponding characterizations in the classes of Orlicz-Lorentz and Orlicz spaces equipped with the Luxemburg norm. We also give a complete description of order continuous Orlicz-Lorentz spaces which contain (order) isometric copies of ℓ1(n) for each integer n≥2. As an application we provide necessary and sufficient conditions for order continuous Orlicz-Lorentz spaces to contain an (order) isometric copy of ℓ1. In particular we give criteria in Orlicz and Lorentz spaces for (order) isometric containment of ℓ1(n) and ℓ1. The results are applied to obtain the description of universal Orlicz-Lorentz spaces for all two-dimensional normed spaces.

18

On perturbed quadratic integral equations and initial value problem with nonlocal conditions in Orlicz spaces

32%

Metwali M. M. A.

Demonstratio Mathematica

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2020

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tom Vol. 53, nr 1

86--94

EN

The existence of a.e. monotonic solutions for functional quadratic Hammerstein integral equations with the perturbation term is discussed in Orlicz spaces. We utilize the strategy of measure of noncompactness related to the Darbo fixed point principle. As an application, we discuss the presence of solution of the initial value problem with nonlocal conditions.