Displaying similar documents to “Remarks on the spaces of differentiable multifunctions”

Fine behavior of functions whose gradients are in an Orlicz space

Jan Malý, David Swanson, William P. Ziemer (2009)

Studia Mathematica

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For functions whose derivatives belong to an Orlicz space, we develop their "fine" properties as a generalization of the treatment found in [MZ] for Sobolev functions. Of particular importance is Theorem 8.8, which is used in the development in [MSZ] of the coarea formula for such functions.

On property (β) of Rolewicz in Musielak-Orlicz sequence spaces equipped with the Orlicz norm

Paweł Kolwicz (2005)

Banach Center Publications

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We prove that the Musielak-Orlicz sequence space with the Orlicz norm has property (β) iff it is reflexive. It is a generalization and essential extension of the respective results from [3] and [5]. Moreover, taking an arbitrary Musielak-Orlicz function instead of an N-function we develop new methods and techniques of proof and we consider a wider class of spaces than in [3] and [5].

Smoothness in Musielak-Orlicz spaces equipped with the Orlicz norm.

Henryk Hudzik, Zenon Zbaszyniak (1997)

Collectanea Mathematica

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A formula for the distance of an arbitrary element x in Musielak-Orlicz space L^Phi from the subspace E^Phi of order continuous elements is given for both (the Luxemburg and the Orlicz) norms. A formula for the norm in the dual space of L^Phi is given for any of these two norms. Criteria for smooth points and smoothness in L^Phi and E^Phi equipped with the Orlicz norm are presented.

Roughness of two norms on Musielak-Orlicz function spaces

Jimin Zheng, Lihuan Sun, Yun'an Cui (2008)

Banach Center Publications

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In this paper, the criteria of strong roughness, roughness and pointwise roughness of Orlicz norm and Luxemburg norm on Musielak-Orlicz function spaces are obtained.

Jung constants of Orlicz sequence spaces

Tao Zhang (2003)

Annales Polonici Mathematici

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Estimation of the Jung constants of Orlicz sequence spaces equipped with either the Luxemburg norm or the Orlicz norm is given. The exact values of the Jung constants of a class of reflexive Orlicz sequence spaces are found by using new quantitative indices for 𝓝-functions.