Multiplier and approximation theorems in Smirnov classes with variable exponent | Zendy

Daniyal ISRAFILZADE | Zendy; Ahmet Testici | Zendy

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Multiplier and approximation theorems in Smirnov classes with variable exponent

Author(s) -

Daniyal ISRAFILZADE,

Ahmet Testici

Publication year - 2018

Publication title -

turkish journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.454

H-Index - 27

eISSN - 1303-6149

pISSN - 1300-0098

DOI - 10.3906/mat-1707-15

Subject(s) - mathematics , lipschitz continuity , bounded function , exponent , corollary , multiplier (economics) , domain (mathematical analysis) , boundary (topology) , inverse , uniqueness , smoothness , characterization (materials science) , pure mathematics , discrete mathematics , combinatorics , mathematical analysis , philosophy , linguistics , economics , macroeconomics , materials science , geometry , nanotechnology

Let G ⊂ C be a bounded Jordan domain with a rectifiable Dini-smooth boundary Γ and let G− := ext Γ. In terms of the higher order modulus of smoothness the direct and inverse problems of approximation theory in the variable exponent Smirnov classes Ep(·)(G) and Ep(·)(G−) are investigated. Moreover, the Marcinkiewicz and Littlewood–Paley type theorems are proved. As a corollary some results on the constructive characterization problems in the generalized Lipschitz classes are presented.

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