Behaviour of $L_{q}$ norms of the $\sinc_{p}$ function
arXiv:1804.034901 citationsh-index: 34
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Provides theoretical insights for researchers working on p-trigonometric functions and related inequalities.
The paper extends Ball's integral inequality to the p-trigonometric setting, providing asymptotic information about the L_q norms of the sinc_p function as q approaches infinity.
An integral inequality due to Ball involves the $L_{q}$ norm of the $\sinc_p$ function; the dependence of this norm on $q$ as $q\rightarrow\infty$ 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 $\sin_{p}.$