Interpolation of nonlinear integral Urysohn operators in net spaces
Сызықтық емес интегралды Урысон операторларының торлы кеңiстiктерiндегi интерполяциясы
Интерполяция нелинейных интегральных операторов Урысона в сетевых пространствах
Kalidolday A.H. Nursultanov E.D.
2022E.A. Buketov Karaganda University Publish house
Bulletin of the Karaganda University. Mathematics Series
2022#105Issue 166 - 73 pp.
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.
interpolation spaces , net spaces , Urysohn integral operators
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L.N. Gumilyov Eurasian National University, Nur-Sultan, Kazakhstan
M.V. Lomonosov Moscow State University (Kazakhstan Branch), Nur-Sultan, Kazakhstan
L.N. Gumilyov Eurasian National University
M.V. Lomonosov Moscow State University (Kazakhstan Branch)
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