BMO- and \(L_p\)-conditions for power series and Dirichlet series with positive coefficients (Q1280266)

It is known that the \(L_p\)-norms of the sums of power series can be estimated from below and above by means of their coefficients, provided these coefficients are nonnegative. The authors prove analogous estimates for the \(L_p\)-norms of the sums of Dirichlet series. Their main result gives exact lower and upper estimates for the BMO-norm of the sums of power series and Dirichlet series, respectively, by means of their coefficients.