An analysis of the convergence problem of a function in functional norms by applying the product Hausdorff operator

Abstract

In this study, we have obtained results regarding the convergence properties
of a function of derived conjugate Fourier series in weighted Lipschitz and
generalized H¨older spaces. These results were obtained by utilizing the product Hausdorff operator. Several intriguing applications of our findings are also examined to observe the convergence behaviour of the function in the aforementioned spaces.