Convergence and Cesaro Summability of the Conjugate Series of a Fourier Series

It is well known that the Gergen criterion [4] which is a generalization of the Lebesgue test is a more powerful criterion than the other existing classical criteria for pointwise convergence of a Fourier series due to Dini, Jordan, Pollard, Young, Hardy and Littlewood, and Lebesgue¹ .