On the existence of entire functions of bounded l-index and l-regular growth - Bordulyak, M. T.; Sheremeta, M. M. (Ukrains’kyi Matematychnyi Zhurnal, 1996)
We prove that, under certain conditions on a positive functionl continuous on [0, +∞], there exists an entire transcendental functionf of boundedl-index such that lnlnM f(r)lnL(r),r→∞, whereM f (r)=max |f(z)|: |z|=r andL(r)=∫ 0 r l(t)dt. Ifl(r)=r p-1 forr≥1, 0