Results 101 to 110 of about 1,287 (117)

Capacity for potentials of functions in Musielak–Orlicz spaces

Nonlinear Analysis: Theory, Methods & Applications, 2011
Let \(\phi(x,t): \mathbb{R}^N\times [0,\infty)\to [0,\infty)\) be a convex function of \(x\), satisfying the \(\Delta_2\)-condition for all \(t\geq 0\), defining a Musiełak-Orlicz space \(L^\phi(G)\), \(G\) being an open set in \(\mathbb{R}^N\). The authors define the \((k,\Phi)\)-capacity of \(E\) relative to \(G\), where \(E\subset\mathbb{R}^N\), by ...
Maeda, Fumi-Yuki, Mizuta, Yoshihiro, Ohno, Takao, Shimomura, Tetsu   +3 more
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On Some Local Geometric Properties in Musielak-Orlicz Function Spaces

Zeitschrift für Analysis und ihre Anwendungen, 2004
Criteria for compactly locally uniformly rotund points in Musielak-Orlicz spaces equipped with the Luxemburg and the Orlicz-Amemiya norms are given. Next, criteria for compact local uniform rotundity and local uniform rotundity of the spaces for both norms are deduced.
Hudzik, Henryk, Kowalewski, Wojciech
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Criteria for complex strongly extreme points of Musielak–Orlicz function spaces

Nonlinear Analysis: Theory, Methods & Applications, 2009
Let \(X\) be a complex Banach space. The authors introduce the notions of complex strongly extreme points, complex midpoint local uniform rotundity, complex locally uniform rotund points. As in the case of real scalars, all these are complex extreme points and any complex locally uniform rotund point is a complex strongly extreme point.
Chen, Lili, Cui, Yunan, Hudzik, Henryk
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Maximal Function Characterizations of Musielak-Orlicz Hardy Spaces

2017
In this chapter, we establish some real-variable characterizations of \(H^{\varphi }(\mathbb{R}^{n})\) in terms of the vertical or the non-tangential maximal functions, via first establishing a Musielak-Orlicz Fefferman-Stein vector-valued inequality.
Dachun Yang, Yiyu Liang, Luong Dang Ky
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Uniform Gateaux differentiability and weak uniform rotundity of Musielak–Orlicz function spaces

Nonlinear Analysis: Theory, Methods & Applications, 2004
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Fang, Liu Li, Fu, Wang Ting, Hudzik, Henryk   +2 more
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SOME LACUNARY DIFFERENCE SEQUENCE SPACES DEFINED BY MUSIELAK–ORLICZ FUNCTIONS

Asian-European Journal of Mathematics, 2011
In this article we introduce the lacunary difference sequence spaces defined by Musielak–Orlicz functions and study their algebraic and topological properties. Also we obtain some relations related to these spaces.
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On S-points of Musielak–Orlicz function spaces

Optik, 2015
Abstract In this paper, criteria for S-points of Musielak–Orlicz function spaces are given. Moreover, as a corollary, the sufficient and necessary conditions for Musielak–Orlicz function spaces to have the S-property are obtained. At last, the conclusions that Musielak–Orlicz function spaces which have the S-property, its dual spaces are ...
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Intrinsic Square Function Characterizations of Musielak-Orlicz Hardy Spaces

2017
In this chapter, for any α ∈ (0, 1] and \(s \in \mathbb{Z}_{+}\), we establish the s-order intrinsic square function characterizations of \(H^{\varphi }(\mathbb{R}^{n})\) by means of the intrinsic Lusin area function S α, s , the intrinsic g-function g α, s or the intrinsic g λ ∗-function g λ, α, s ∗ with the best known range λ ∈ (2 + 2(α + s)∕n ...
Dachun Yang, Yiyu Liang, Luong Dang Ky
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Gagliardo–Nirenberg inequality for generalized Riesz potentials of functions in Musielak-Orlicz spaces

Archiv der Mathematik, 2012
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Mizuta, Yoshihiro, Nakai, Eiichi, Sawano, Yoshihiro, Shimomura, Tetsu   +3 more
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Points of monotonicity in Musielak--Orlicz function spaces endowed with the Orlicz norm

Publicationes Mathematicae Debrecen, 2002
Let \((X,\|\cdot\|,\leq)\) be a Banach lattice, let \(X^+\) denote the positive cone in \(X\) and let \(S(X)\) be the unit sphere of \(X\). A point \(x\in S(X^+)\) is said to be upper (lower) monotone if for any \(y\in X^+\backslash\{0\},\) (any \(y\in X^+\backslash \{0\}, y\leq x)\) there holds \(\|x+y\|>1,(\|x-y\|
Hudzik, H., Liu, Xin Bo, Wang, T.
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