On some questions of topology for S-valued fractional Sobolev spaces.
H1/2 maps with values into the circle : minimal connections, lifting, and the Ginzburg–Landau equation
A new function space and applications
We define a new function space , which contains in particular BMO, BV, and , . We investigate its embedding into Lebesgue and Marcinkiewicz spaces. We present several inequalities involving norms of integer-valued functions in . We introduce a significant closed subspace, , of , containing in particular VMO and , . The above mentioned estimates imply in particular that integer-valued functions belonging to are necessarily constant. This framework provides a “common roof” to various,...
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