Approximation in weighted generalized grand Lebesgue spaces
Volume 143 / 2016
Colloquium Mathematicum 143 (2016), 113-126 MSC: Primary 41A10, 41A30; Secondary 42A10. DOI: 10.4064/cm6555-12-2015 Published online: 3 December 2015
The direct and inverse problems of approximation theory in the subspace of weighted generalized grand Lebesgue spaces of $2\pi $-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.