Autor: Foralewski, Paweł - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Some remarks on level functions and their applications
Autorzy:: Foralewski, Paweł
Leśnik, Karol
Maligranda, Lech
Powiązania:: https://bibliotekanauki.pl/articles/745238.pdf
Data publikacji:: 2016
Wydawca:: Polskie Towarzystwo Matematyczne
Tematy:: level functions, dual spaces, Orlicz−Lorentz spaces, Halperin spaces, Cesàro spaces
Opis:: A comparison of the level functions considered by Halperin and Sinnamon is discussed. Moreover, connections between Lorentz-type spaces, down spaces, Cesàro spaces, and Sawyer's duality formula are explained. Applying Sinnamon's ideas, we prove the duality theorem for Orlicz−Lorentz spaces which generalizes a recent result by Kamińska, Leśnik, and Raynaud (and Nakamura). Finally, some applications of the level functions to the geometry of Orlicz−Lorentz spaces are presented.
Źródło:: Commentationes Mathematicae; 2016, 56, 1
0373-8299
Pojawia się w:: Commentationes Mathematicae
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: Characteristic of monotonicity of Orlicz function spaces equipped with the Orlicz norm
Autorzy:: Foralewski, Paweł
Hudzik, Henryk
Kaczmarek, Radosław
Krbec, Miroslav
Powiązania:: https://bibliotekanauki.pl/articles/746439.pdf
Data publikacji:: 2013
Wydawca:: Polskie Towarzystwo Matematyczne
Tematy:: Orlicz space
Orlicz norm
Kothe space
Kothe dual
characteristic of monotonicity
strict monotonicity
point of order smoothness
Opis:: 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.
Źródło:: Commentationes Mathematicae; 2013, 53, 2
0373-8299
Pojawia się w:: Commentationes Mathematicae
Dostawca treści:: Biblioteka Nauki

Artykuł

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