On direct estimates and approximation results by the kantorovich operators in weighted grand lebesgue spaces

Abstract

We give some new embeddings results for weighted grand Lebesgue spaces (formula presented), where (formula presented) is a open bounded subset. We also obtain the boundedness of the Kantorovich operator Kn in (formula presented) [0, 1]. In addition, we establish two direct estimates by K-functionals of the rate of approximation in (formula presented) [0, 1]. We generalize the direct estimate inequality in classical Lebesgue spaces (formula presented) [0, 1] to (formula presented) [0, 1] using the boundedness of the Hardy-Littlewood maximal operator in (formula presented) [0, 1]. Finally, we obtain similar results in [8] for the spaces (formula presented) [0, 1] .