UNIFORM MEAN VALUE ESTIMATES AND DISCRETE HILBERT INEQUALITIES VIA ORTHOGONAL DIRICHLET SERIES

摘要

Let {λ_j}_j~∞=0 be a strictly increasing sequence of positive numbers with λ0 = 0 and λ1 = 1. We use orthogonal Dirichlet polynomials associated with the arctangent density, to observe that for r > 0, when the right-hand side converges. As a consequence, we obtain uniform mean value estimates, discrete Hilbert type inequalities, and asymptotics as r→∞ for classes of Dirichlet series.