Indices of Orlicz spaces and some applications. (English) Zbl 0937.46023
Summary: We study connections between the Boyd indices in Orlicz spaces and the growth conditions frequently met in various applications, for instance, in the regularity theory of variational integrals with non-standard growth. We develop a truncation method for computation of the indices and we also give characterizations of them in terms of the growth exponents and of the Jensen means. Applications concern variational integrals and extrapolation of integral operators.
MSC:
| 46E30 | Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) |
| 26A12 | Rate of growth of functions, orders of infinity, slowly varying functions |
| 35A15 | Variational methods applied to PDEs |
| 35B10 | Periodic solutions to PDEs |
| 42B20 | Singular and oscillatory integrals (Calderón-Zygmund, etc.) |
| 46E35 | Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems |
