Abstract:
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.
Citation:
D. M. Stolyarov, “On Embedding of Besov Spaces of Zero Smoothness into Lorentz Spaces”, Theory of Functions of Several Real Variables and Its Applications, Collected papers. Dedicated to Oleg Vladimirovich Besov on the occasion of his 90th birthday, Trudy Mat. Inst. Steklova, 323, Steklov Mathematical Institute of RAS, Moscow, 2023, 204–212; Proc. Steklov Inst. Math., 323 (2023), 197–205
\Bibitem{Sto23}
\by D.~M.~Stolyarov
\paper On Embedding of Besov Spaces of Zero Smoothness into Lorentz Spaces
\inbook Theory of Functions of Several Real Variables and Its Applications
\bookinfo Collected papers. Dedicated to Oleg Vladimirovich Besov on the occasion of his 90th birthday
\serial Trudy Mat. Inst. Steklova
\yr 2023
\vol 323
\pages 204--212
\publ Steklov Mathematical Institute of RAS
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm4343}
\crossref{https://doi.org/10.4213/tm4343}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2023
\vol 323
\pages 197--205
\crossref{https://doi.org/10.1134/S0081543823050127}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85186881428}
Citation in format AMSBIB
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