Perturbation Method in Orlicz Sequence Spaces

We develop a new perturbation method in Orlicz sequence spaces ${\ell }_M$ $\ell _{M}$ with Orlicz function $M$ $M$ satisfying ${\mathrm{\Delta }}_2$ $\Delta _{2}$ condition at zero. This result allows one to support from below any bounded below lower semicontinuous function with bounded support, with a perturbation of the defining function ${\sigma }_M$ $\sigma _{M}$ .

We give few examples how the method can be used for determining the type of the smoothness of certain Orlicz spaces.