Geodesic
Criteria for embedding of generalized Bessel and Riesz potential spaces in rearrangement invariant spaces
Eurasian mathematical journal, Tome 10 (2019) no. 2, pp. 8-29

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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. 
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     author = {N. A. Bokayev and M. L. Goldman and G. Zh. Karshygina},
     title = {Criteria for embedding of generalized {Bessel} and {Riesz} potential spaces in rearrangement invariant spaces},
     journal = {Eurasian mathematical journal},
     pages = {8--29},
     publisher = {mathdoc},
     volume = {10},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EMJ_2019_10_2_a0/}
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N. A. Bokayev; M. L. Goldman; G. Zh. Karshygina. Criteria for embedding of generalized Bessel and Riesz potential spaces in rearrangement invariant spaces. Eurasian mathematical journal, Tome 10 (2019) no. 2, pp. 8-29. http://geodesic.mathdoc.fr/item/EMJ_2019_10_2_a0/