Interpolation Properties of Certain Classes of Net Spaces
Kalidolday A. Nursultanov E.
May 2023Pleiades Publishing
Lobachevskii Journal of Mathematics
2023#44Issue 51870 - 1878 pp.
Abstract: The paper studies the interpolation properties of net spaces N_{p,q}(M) , when M is the set of dyadic cubes in mathbb{R}^{n} , and also when M is the family of all cubes with parallel faces to the coordinate axes in mathbb{R}^{n} . It is shown that, in the case when M is the set of dyadic cubes the scale of spaces is closed with respect to the real interpolation method. In the case, when M is the set of all cubes with parallel faces to the coordinate axes, an analogue of the Marcinkiewicz–Calderon theorem on cones of non-negative functions is given.
interpolation properties of net spaces , net spaces
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Institute of Mathematics and Mathematical Modeling, Almaty, 050010, Kazakhstan
Lomonosov Moscow State University (Kazakhstan Branch), Astana, 010010, Kazakhstan
Institute of Mathematics and Mathematical Modeling
Lomonosov Moscow State University (Kazakhstan Branch)
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