On approximation of bivariate functions by Abel–Poisson and conjugate Abel–Poisson means

Firstly, we determine the degree of approximation of a bivariate periodic function by double Abel–Poisson mean of its double Fourier series in the metric of a particular Zygmund’s space. Secondly, knowing that a double Fourier series has three double conjugate series, we show the degree of approximation for one of bivariate conjugate function in \(L^p\) $L^p$ -metric by its corresponding double Abel–Poisson means of the double conjugate series. Finally, we establish two propositions on the degree of approximation of other two double conjugate Abel–Poisson means itself (in \(L^p\) $L^p$ -metric) by some specific quantities.