Lower bound for the best approximations of periodic summable functions of two variables and their conjugates in terms of Fourier coefficients

Abstract

In terms of Fourier coefficients, we establish lower bounds for the sum of norms and the sum of the best approximations by trigonometric polynomials for functions from the space L(Q²) and functions conjugate to them with respect to each variable and with respect to both variables, provided that these functions are summable.