The generalized monotonicity class and integrability of power series

Sergey Volosivets; Valery Krivobok

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Displaying similar documents to “The generalized monotonicity class and integrability of power series”

Monotone coefficients and monotonicity of Orlicz spaces.

Yanming Lü, Junming Wang, Tingfu Wang (1999)

Revista Matemática Complutense

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The criteria for uniform monotonicity, locally uniformly monotonicity and monotonicity of of Orlicz spaces with Luxemburg and Orlicz norms are given. The monotone coefficients of a point and of the spaces are computed.

Integrability theorems for power series

Babu Ram (1974)

Colloquium Mathematicae

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Approximation by trigonometric polynomials in weighted Orlicz spaces

Daniyal M. Israfilov, Ali Guven (2006)

Studia Mathematica

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We investigate the approximation properties of the partial sums of the Fourier series and prove some direct and inverse theorems for approximation by polynomials in weighted Orlicz spaces. In particular we obtain a constructive characterization of the generalized Lipschitz classes in these spaces.

Strictly and uniformly monotone sequential Musielak-Orlicz spaces.

W. Kurc (1999)

Collectanea Mathematica

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New Orlicz variants of Hardy type inequalities with power, power-logarithmic, and power-exponential weights

Agnieszka Kałamajska, Katarzyna Pietruska-Pałuba (2012)

Open Mathematics

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We obtain Hardy type inequalities $\int_{0}^{\infty} M (ω (r) |u (r)|) ρ (r) d r ⩽ C_{1} \int_{0}^{\infty} M (|u (r)|) ρ (r) d r + C_{2} \int_{0}^{\infty} M (|u^{'} (r)|) ρ (r) d r,$ and their Orlicz-norm counterparts ${∥ω u∥}_{L^{M} (ℝ_{+}, ρ)} ⩽ {\tilde{C}}_{1} {∥u∥}_{L^{M} (ℝ_{+}, ρ)} + {\tilde{C}}_{2} {∥u^{'}∥}_{L^{M} (ℝ_{+}, ρ)},$ with an N-function M, power, power-logarithmic and power-exponential weights ω, ρ, holding on suitable dilation invariant supersets of C 0∞(ℝ+). Maximal sets of admissible functions u are described. This paper is based on authors’ earlier abstract results and applies them to particular classes of weights.

A multiplier theorem on weighted Orlicz spaces

Bordin, B., Garcia, J.B. (1991)

Portugaliae mathematica

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Some gap power series in multidimensional setting

Józef Siciak (2011)

Annales UMCS, Mathematica

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We study extensions of classical theorems on gap power series of a complex variable to the multidimensional case.

Some gap power series in multidimensional setting

Józef Siciak (2011)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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We study extensions of classical theorems on gap power series of a complex variable to the multidimensional case.

Best Constants for the Inequalities between Equivalent Norms in Orlicz Spaces

Ha Huy Bang, Nguyen Van Hoang, Vu Nhat Huy (2011)

Bulletin of the Polish Academy of Sciences. Mathematics

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We investigate best constants for inequalities between the Orlicz norm and Luxemburg norm in Orlicz spaces.

Moduli and characteristics of monotonicity in some Banach lattices.

Foralewski, Paweł, Hudzik, Henryk, Kaczmarek, Radosław, Krbec, Miroslav (2010)

Fixed Point Theory and Applications [electronic only]

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Remarks on a moment problem and a problem of perfection of power methods of limitation

Andrzej Birkholc (1971)

Colloquium Mathematicae

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On a class of universal Orlicz function spaces

César Ruiz (1990)

Acta Universitatis Carolinae. Mathematica et Physica

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Gagliardo-Nirenberg inequalities in weighted Orlicz spaces

Agnieszka Kałamajska, Katarzyna Pietruska-Pałuba (2006)

Studia Mathematica

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We derive inequalities of Gagliardo-Nirenberg type in weighted Orlicz spaces on ℝⁿ, for maximal functions of derivatives and for the derivatives themselves. This is done by an application of pointwise interpolation inequalities obtained previously by the first author and of Muckenhoupt-Bloom-Kerman-type theorems for maximal 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].

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.

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.

Compact Embeddings for Weighted Orlicz-Sobolev Spaces on IRN.

Pierre-A. Vuillermot (1987/88)

Mathematische Annalen

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