Geodesic
On Embedding of Besov Spaces of Zero Smoothness into Lorentz Spaces
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Theory of Functions of Several Real Variables and Its Applications, Tome 323 (2023), pp. 204-212

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We show that the zero smoothness Besov space $B_{p,q}^{0,1}$ does not embed into the Lorentz space $L_{p,q}$ unless $p=q$; here $p,q\in (1,\infty )$. This answers in the negative a question posed by O. V. Besov.
Mots-clés : Besov space
Keywords: embedding theorem. 
@article{TM_2023_323_a11,
     author = {D. M. Stolyarov},
     title = {On {Embedding} of {Besov} {Spaces} of {Zero} {Smoothness} into {Lorentz} {Spaces}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {204--212},
     publisher = {mathdoc},
     volume = {323},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2023_323_a11/}
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D. M. Stolyarov. On Embedding of Besov Spaces of Zero Smoothness into Lorentz Spaces. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Theory of Functions of Several Real Variables and Its Applications, Tome 323 (2023), pp. 204-212. http://geodesic.mathdoc.fr/item/TM_2023_323_a11/