Behaviour of $L_q$ norms of the $\sinc_{p}$ function

Abstract

An integral inequality due to Ball involves the $L_q$ norm of the $\sinc_p$ function; the dependence of this norm on $q$ as $q\to \infty$ is now understood. By use of recent inequalities involving $p-$trigonometric functions $(1<p<\infty )$ we obtain asymptotic information about the analogue of Ball's integral when $\sin$ is replaced by ${\sin }_p.$

11 pages