John-Nirenberg inequality for Riemann type series

Abstract

We obtain an improvement of the John-Nirenberg inequality for the series of the form ${\sum }_{n=1}^{\infty }{n}^{-1}{e}^{2\pi i{n}^{k}x},k>2,$ on intervals consisting of points of a same convergent of their continued fractions. We also establish a convergence criterion for these series.

11 pages

References in corpus (1)

• Fourier series in BMO with number theoretical implications