Approximation by matrix transforms in weighted Orlicz spaces

Authors: SADULLA JAFAROV

Abstract: In this work the approximation problems of the functions by matrix transforms in weighted Orlicz spaces with Muckenhoupt weights are studied.We obtain the degree of approximation of functions belonging to Lipschitz class $Lip(\alpha ,M,\omega )$ through matrix transforms $% T_{n}^{\left( A\right) }(x,f)$,$~$and Nörlund means $N_{n}\left(x,f\right) ~$of their trigonometric Fourier series.

Keywords: Matrix transforms, trigonometric approximation, Orlicz space, weighted Orlicz space, Boyd indices, Muckenhoupt weight, modulus of smoothness, weighted Lipschitz classes

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