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