Interpolation of nonlinear integral Urysohn operators in net spaces
Abstrak
In this paper, we study the interpolation properties of the net spaces Np,q(M), in the case when M is a sufficiently general arbitrary system of measurable subsets from Rn. The integral Urysohn operator is considered. This operator generalizes all linear, integral operators, and non-linear integral operators. The Urysohn operator is not a quasilinear or subadditive operator. Therefore, the classical interpolation theorems for these operators do not hold. A certain analogue of the Marcinkiewicz-type interpolation theorem for this class of operators is obtained. This theorem allows to obtain, in a sense, a strong estimate for Urysohn operators in net spaces from weak estimates for these operators in net spaces with local nets. For example, in order for the Urysohn integral operator in a net space, where the net is the set of all balls in Rn , it is sufficient for it to be of weak type for net spaces, where the net is concentric balls.
Topik & Kata Kunci
Penulis (2)
A.H. Kalidolday
E.D. Nursultanov
Akses Cepat
- Tahun Terbit
- 2022
- Sumber Database
- DOAJ
- DOI
- 10.31489/2022m1/66-73
- Akses
- Open Access ✓