Abstract We establish an analogue of Pitt’s inequality for Fourier series on Tᵈ T d, extending the range of parameters by employing averages of Fourier coefficients. We show that this inequality is closely connected to sharp estimates for the Lₚ L p norms of the Dirichlet kernels over various subsets of Zᵈ Z d.
Нурсултанов et al. (Wed,) studied this question.