Lower and upper estimations of the modulus of convexity in some Orlicz spaces (Q803474)

Lower and upper estimations of the modulus of convexity for Orlicz spaces generated by Orlicz functions such that their compositions with the square root are convex functions in \({\mathbb{R}}_+\) are given in terms of Lindberg and Simonenko indices. Consequently, a calculation of the modulus in a class of Orlicz spaces essentially wider than the class of Lebesgue spaces \(L^ p\), \(2\leq p<+\infty\) is obtained. Finally, some remarks and examples are given.