### On some questions of topology for S-valued fractional Sobolev spaces.

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We define a new function space $B$, which contains in particular BMO, BV, and ${W}^{1/p,p}$, $1<p<\infty $. We investigate its embedding into Lebesgue and Marcinkiewicz spaces. We present several inequalities involving ${L}^{p}$ norms of integer-valued functions in $B$. We introduce a significant closed subspace, ${B}_{0}$, of $B$, containing in particular VMO and ${W}^{1/p,p}$, $1\le p<\infty $. The above mentioned estimates imply in particular that integer-valued functions belonging to ${B}_{0}$ are necessarily constant. This framework provides a “common roof” to various,...

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