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

100%

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

Commentationes Mathematicae

2013

tom 53

nr 2

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.

Some remarks on level functions and their applications

100%

Foralewski P., Leśnik K., Maligranda L.

Commentationes Mathematicae

2016

tom 56

nr 1

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.

Ograniczanie wyników

2 Commentationes Mathematicae

2 Foralewski P.

1 Hudzik H.

1 Kaczmarek R.

1 Krbec M.

1 Leśnik K.

1 Maligranda L.

1 2016

1 2013

Wyniki wyszukiwania

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

Some remarks on level functions and their applications