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May 15, 2026Open Access

Pitt’s Inequalities and Bounds for Dirichlet Kernels

Key Points

The study aims to develop an analogue of Pitt’s inequality for Fourier series on multidimensional tori.
Employed averages of Fourier coefficients to extend parameter ranges.
Analyzed the relationship between Pitts inequality and lp norms of Dirichlet kernels.
Examined sharp estimates across various subsets of Zd.
Established a new inequality connecting Fourier coefficients and lp norms.
Provided precise bounds for Dirichlet kernels that extend previous results.

Abstract

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.

Pitt’s Inequalities and Bounds for Dirichlet Kernels

Key Points

Abstract

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