Behaviour of exponential means of Fourier series and conjugated Fourier series in Lebesgue points
In the present paper the researches consider the behavior of the class of operators defined by exponential summing methods of Fourier series. The authors examine exponential means of certain Fourier series. The convergence in Lebesgue points is investigated. The operators determined by the convergence are known as the means of Poisson - Abel and they play the substantial role in different questions of the analysis. Though even the most simple and natural extension is not fully investigated. Conclusions of the considered theorem follow from the results for general infinite convex or piecewise convex summing sequences; the given results are also of individual interest. The analogue of the theorem is specified for exponential means of conjugate Fourier series. The examples of exponential means are given, which satisfy the hypotheses of the considered theorems and are also of individual interest. The obtained results are valid, in particular, for the generalized Poisson means. The authors also give an example of a polynomial-exponential method of summation.