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Orlicz spaces, α-decreasing functions, and the Δ₂ condition

Gary M. Lieberman (2004)

Colloquium Mathematicae

We prove some quantitatively sharp estimates concerning the Δ₂ and ∇₂ conditions for functions which generalize known ones. The sharp forms arise in the connection between Orlicz space theory and the theory of elliptic partial differential equations.

Orlicz-Morrey spaces and the Hardy-Littlewood maximal function

Eiichi Nakai (2008)

Studia Mathematica

We prove basic properties of Orlicz-Morrey spaces and give a necessary and sufficient condition for boundedness of the Hardy-Littlewood maximal operator M from one Orlicz-Morrey space to another. For example, if f ∈ L(log L)(ℝⁿ), then Mf is in a (generalized) Morrey space (Example 5.1). As an application of boundedness of M, we prove the boundedness of generalized fractional integral operators, improving earlier results of the author.

Orthogonally additive functionals on B V

Khaing Aye Khaing, Peng Yee Lee (2004)

Mathematica Bohemica

In this paper we give a representation theorem for the orthogonally additive functionals on the space B V in terms of a non-linear integral of the Henstock-Kurzweil-Stieltjes type.

Orthonormal bases for spaces of continuous and continuously differentiable functions defined on a subset of Zp.

Ann Verdoodt (1996)

Revista Matemática de la Universidad Complutense de Madrid

Let K be a non-Archimedean valued field which contains Qp, and suppose that K is complete for the valuation |·|, which extends the p-adic valuation. Vq is the closure of the set {aqn | n = 0,1,2,...} where a and q are two units of Zp, q not a root of unity. C(Vq --> K) (resp. C1(Vq --> K)) is the Banach space of continuous functions (resp. continuously differentiable functions) from Vq to K. Our aim is to find orthonormal bases for C(Vq --> K) and C1(Vq --> K).

Ostrowski Type Inequalities over Spherical Shells

Anastassiou, George A. (2008)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 26D10, 26D15.Here are presented Ostrowski type inequalities over spherical shells. These regard sharp or close to sharp estimates to the difference of the average of a multivariate function from its value at a point.

Ostrowski’s type inequalities for complex functions defined on unit circle with applications for unitary operators in Hilbert spaces

S.S. Dragomir (2015)

Archivum Mathematicum

Some Ostrowski’s type inequalities for the Riemann-Stieltjes integral a b f e i t d u t of continuous complex valued integrands f : 𝒞 0 , 1 defined on the complex unit circle 𝒞 0 , 1 and various subclasses of integrators u : a , b 0 , 2 π of bounded variation are given. Natural applications for functions of unitary operators in Hilbert spaces are provided as well.

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