This article is cited in 8 papers

Criteria for embedding of generalized Bessel and Riesz potential spaces in rearrangement invariant spaces

N. A. Bokayev^a, M. L. Goldman^b, G. Zh. Karshygina<sup>a

a</sup> Department of Mechanics and Mathematics, L.N. Gumilyov Eurasian National University, 5 Munaitpasov St, 010008 Nur-Sultan, Kazakhstan
^b Institute of Mathematics, Peoples’ Friendship University of Russia (RUDN University), 6 Mikluho-Maklaya St, 117198 Moscow, Russia

Abstract: We consider the spaces of generalized Bessel and Riesz potentials and establish criteria for the embedding of these spaces in rearrangements invariant spaces. To do this we obtain constructive equivalent descriptions for the cones of decreasing rearrangement of potentials. Covering and equivalence of cones are studied with respect to order relations which allows to weaken substantially the assumptions on the kernels of potentials.

Keywords and phrases: functional norm, cones of functions with monotonicity conditions, embedding of potential spaces in rearrangement-invariant spaces, generalized Bessel and Riesz potentials.

MSC: 46E30, 42A16

Received: 29.06.2018

Language: English

DOI: 10.32523/2077-9879-2019-10-2-08-29

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