TITLE

# Extension of The Best Approximation Operator in Orlicz Spaces

AUTHOR(S)
Carrizo, Ivana; Favier, Sergio; Zó, Felipe
PUB. DATE
January 2008
SOURCE
Abstract & Applied Analysis;2008, p1
SOURCE TYPE
DOC. TYPE
Article
ABSTRACT
Let (Î©,A, Î¼) be a probability space and L ? A a sub-Ïƒ-lattice of the Ïƒ-algebra A. We study an extension of the best Ï•-approximation operator from an Orlicz space LÏ• to the space LÏ•' , where Ï•' denotes the derivative of the convex, but not necessarily a strictly convex function Ï•. We obtain convergence results when a sequence of Ïƒ-algebras Bn converges to Bâˆž in a suitable way.
ACCESSION #
36264813

## Related Articles

• Hardyâ€“Orlicz Spaces and Their Multiplication Operators. Lu, Qun; Cao, Guang; Liu, Li // Acta Mathematica Sinica;Jun2005, Vol. 21 Issue 3, p593

In this paper some formulae on the relationship between Hardy and Hardyâ€“Orlicz spaces are presented, and multiplication operators on Hardyâ€“Orlicz spaces are discussed.

• Approximating Polynomials for Functions of Weighted Smirnov-Orlicz Spaces. Akgün, Ramazan // Journal of Function Spaces & Applications;2012, p1

Let G0 and Gâˆž be, respectively, bounded and unbounded components of a plane curve Î“ satisfying Dini's smoothness condition. In addition to partial sum of Faber series of f belonging to weighted Smirnov-Orlicz space EM,? G0), we prove that interpolating polynomials and Poisson...

• Simultaneous proximinality of vector valued function spaces. Khandaqji, Mona; Awawdeh, Fadi; Jawdat, Jamila // Turkish Journal of Mathematics;Sep2012, Vol. 36 Issue 3, p437

A characterization of best simultaneous approximation of KÃ¶othe spaces of vector-valued functions is given. This characterization is a generalization of some analogous theorems for Orlicz Bochner spaces.

• Fenchel's Duality Theorem for Nearly Convex Functions. Boţ, R. I.; Grad, S. M.; Wanka, G. // Journal of Optimization Theory & Applications;Mar2007, Vol. 132 Issue 3, p509

We present an extension of Fenchel's duality theorem by weakening the convexity assumptions to near convexity. These weak hypotheses are automatically fulfilled in the convex case. Moreover, we show by a counterexample that a further extension to closely convex functions is not possible under...

• PRODUCT-TYPE OPERATORS FROM WEIGHTED BERGMAN-ORLICZ SPACES TO BLOCH-ORLICZ SPACES. HONG-BIN BAI; ZHI-JIE JIANG // Journal of Computational Analysis & Applications;12/15/2016, Vol. 21 Issue 7, p1147

Let D = {z Ïµ C : Ç€zÇ€ < 1g be the open unit disk, ' an analytic self-map of D and an analytic function on D. Let D be the differentiation operator and WÏ†Ïˆ the weighted composition operator. The boundedness and compactness of the product-type operators DWÏ†Ïˆ from the...

• A Characterization of Best ?-Approximants with Applications to Multidimensional Isotonic Approximation. Mazzone, F. D.; Cuenya, H. H. // Constructive Approximation;2005, Vol. 21 Issue 2, p207

Some properties of best monotone approximants in several variables are obtained. We prove the following abstract characterization theorem. Let $(\om, {\cal A},\mu)$ be a measurable space and let ${\cal L}\subset{\cal A}$ be a $\sigma$-lattice. If $f$ belongs to a Musielak-Orlicz space...

• Improved Converse Theorems and Fractional Moduli of Smoothness in Orlicz Spaces. AKGÜN, RAMAZAN // Bulletin of the Malaysian Mathematical Sciences Society;2013, Vol. 36 Issue 1, p49

In the present work converse theorems of trigonometric approximation of functions and its fractional derivatives in certain Orlicz spaces are improved with respect to the fractional moduli of smoothness. An improved Marchaud inequality is also given.

• Asymptotically double lacunry equivalent sequences defined by Orlicz functions. Esi, Ayhan // Acta Scientiarum: Technology;Apr-Jun2014, Vol. 36 Issue 2, p323

This paper presents the following definition which is natural combination of the definition for asymptotically equivalent and Orlicz function. The two nonnegative double sequences Ï°= (xk,l ) y=(yk,l) , = and Ï° =(y k, l Î³) are said to be M-asymptotically double equivalent to multiple L...

• COMPOSITION OPERATOR ON ZYGMUND-ORLICZ SPACE. NING XU; ZE-HUA ZHOU // Journal of Computational Analysis & Applications;Jun2016, Vol. 20 Issue 6, p1058

In this paper, we use Young's function to define Zygmund-Orlicz space. We study boundedness and compactness of composition operator on Zygmund-Orlicz space.

Share