Wyniki wyszukiwania

1

On a converse inequality for maximal functions in Orlicz spaces

100%

Kita H.

Studia Mathematica

|

1996

|

tom 118

|

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 $⨍ ∈ L^{1}(𝕋)$.

2

Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik

Summing multi-norms defined by Orlicz spaces and symmetric sequence space

80%

Blasco O.

Commentationes Mathematicae

|

2016

|

tom 56

|

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 $E=\ell_r$.

3

Boundedness of Toeplitz type operators associated to Riesz potential operator with general kernel on Orlicz space

70%

Chen D.

Open Mathematics

|

2015

|

tom 13

|

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.

4

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

5

Characteristic of monotonicity of Orlicz function spaces equipped with the Orlicz norm

61%

Foralewski P., Hudzik H., Kaczmarek R., Krbec M.

Commentationes Mathematicae

|

2013

|

tom 53

|

nr 2

EN

We first prove that the property of strict monotonicity of a~K\"othe space $(E,\|.\|_E)$ and\slash or of its K\"othe dual $(E',\|.\|_{E'})$ can be used successfully to compare the supports of $x\in E\backslash\{\theta\}$ and $y\in S(E')$, where $=\|x\|_E$. Next we prove that any element $x\in S_{+}(E)$ with $\mu(T\backslash\operatorname{supp} x)=0$ is a~point of order smoothness in $E$, whenever $E$ is an order continuous K\"othe space. Finally, we present formulas for the characteristic of monotonicity of Orlicz function spaces endowed with the Orlicz norm in the case when the generating Orlicz function does not satisfy suitable $\Delta_2$-condition or the measure is non-atomic infinite, and some lower and upper estimates for the characteristic of monotonicity of this spaces when the measure is non-atomic and finite.

6

A description of Banach space-valued Orlicz hearts

51%

Labuschagne C., Offwood T.

Open Mathematics

|

2010

|

tom 8

|

nr 6

1109-1119

EN

Let Y be a Banach space, (Ω, Σ; μ) a probability space and φ a finite Young function. It is shown that the Y-valued Orlicz heart H φ(μ, Y) is isometrically isomorphic to the l-completed tensor product $$ H_\varphi \left( \mu \right)\tilde \otimes _l Y $$ of the scalar-valued Orlicz heart Hφ(μ) and Y, in the sense of Chaney and Schaefer. As an application, a characterization is given of the equality of $$ \left( {H_\varphi \left( \mu \right)\tilde \otimes _l Y} \right)* $$ and $$ H_\varphi \left( \mu \right)*\tilde \otimes _l Y* $$ in terms of the Radon-Nikodým property on Y. Convergence of norm-bounded martingales in H φ(μ, Y) is characterized in terms of the Radon-Nikodým property on Y. Using the associativity of the l-norm, an alternative proof is given of the known fact that for any separable Banach lattice E and any Banach space Y, E and Y have the Radon-Nikodým property if and only if $$ E\tilde \otimes _l Y $$ has the Radon-Nikodým property. As a corollary, the Radon-Nikodým property in H φ(μ, Y) is described in terms of the Radon-Nikodým property on H φ(μ) and Y.

7

On the Existence of Common Fixed Points for Semigroups of Nonlinear Mappings in Modular Function Spaces

51%

Kozlowski W. M.

Commentationes Mathematicae

|

2011

|

tom 51

|

nr 1

EN

Let $C$ be a $\rho$-bounded, $\rho$-closed, convex subset of a modular function space $L_\rho$. We investigate the existence of common fixed points for semigroups of nonlinear mappings $T_t\colon C\to C$, i.e. a family such that $T_0(x) = x$, $T_{s+t} = T_s (T_t (x))$, where each $T_t$ is either $\rho$-contraction or $\rho$-nonexpansive. We also briefly discuss existence of such semigroups and touch upon applications to differential equations.

Ograniczanie wyników

3 Commentationes Mathematicae

2 Open Mathematics

1 Colloquium Mathematicum

1 Studia Mathematica

1 Appelli J.

1 Blasco O.

1 Chen D.

1 Foralewski P.

1 Hudzik H.

1 Kaczmarek R.

1 Kalitvin A. S.

1 Kita H.

1 Kozlowski W. M.

1 Krbec M.

1 Labuschagne C.

1 Offwood T.

1 Zabreĭko P. P.

1 2016

1 2015

1 2013

1 2011

1 2010

1 1998

1 1996

On a converse inequality for maximal functions in Orlicz spaces

Summing multi-norms defined by Orlicz spaces and symmetric sequence space

Boundedness of Toeplitz type operators associated to Riesz potential operator with general kernel on Orlicz space

Partial integral operators in Orlicz spaces with mixed norm

Characteristic of monotonicity of Orlicz function spaces equipped with the Orlicz norm

A description of Banach space-valued Orlicz hearts

On the Existence of Common Fixed Points for Semigroups of Nonlinear Mappings in Modular Function Spaces