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Approximation by p -Faber-Laurent rational functions in the weighted Lebesgue spaces

Daniyal M. Israfilov (2004)

Czechoslovak Mathematical Journal

Let L C be a regular Jordan curve. In this work, the approximation properties of the p -Faber-Laurent rational series expansions in the ω weighted Lebesgue spaces L p ( L , ω ) are studied. Under some restrictive conditions upon the weight functions the degree of this approximation by a k th integral modulus of continuity in L p ( L , ω ) spaces is estimated.

Approximation in weighted generalized grand Lebesgue spaces

Daniyal M. Israfilov, Ahmet Testici (2016)

Colloquium Mathematicae

The direct and inverse problems of approximation theory in the subspace of weighted generalized grand Lebesgue spaces of 2π-periodic functions with the weights satisfying Muckenhoupt's condition are investigated. Appropriate direct and inverse theorems are proved. As a corollary some results on constructive characterization problems in generalized Lipschitz classes are presented.

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