Orlicz spaces associated to a quasi-Banach function space: applications to vector measures and interpolation
2020
The Orlicz spaces
$$X^{\varPhi }$$
associated to a quasi-Banach function space X are defined by replacing the role of the space
$$L^1$$
by X in the classical construction of Orlicz spaces. Given a vector measure m, we can apply this construction to the spaces
$$L^1_w(m),$$
$$L^1(m)$$
and
$$L^1(\Vert m\Vert )$$
of integrable functions (in the weak, strong and Choquet sense, respectively) in order to obtain the known Orlicz spaces
$$L^{\varPhi }_w(m)$$
and
$$L^{\varPhi }(m)$$
and the new ones
$$L^{\varPhi }(\Vert m\Vert ).$$
Therefore, we are providing a framework where dealing with different kind of Orlicz spaces in a unified way.
Some applications to complex interpolation are also given.
Keywords:
- Correction
- Source
- Cite
- Save
- Machine Reading By IdeaReader
19
References
2
Citations
NaN
KQI