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The \(\infty\)-Besov capacity problem. (English) Zbl 1383.31005

Summary: A theory of \(\infty\)-Besov capacities is developed and several applications are provided. In particular, we solve an open problem in the theory of limits of the \(\infty\)-Besov semi-norms, we obtain new restriction-extension inequalities, and we characterize the pointwise multipliers acting on the \(\infty\)-Besov spaces.

MSC:

31C15 Potentials and capacities on other spaces
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
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