We study when characteristic and H\"older continuous functions are traces of Sobolev functions on doubling metric measure spaces. We provide analytic and geometric conditions sufficient for extending characteristic and H\"older continuous functions into globally defined Sobolev functions.

Keywords:

characteristic function, Newtonian function, metric space, resolutivity, Hölder continuous, Perron solution, $p$-harmonic, Sobolev extension, Whitney covering characteristic function, Newtonian function, metric space, resolutivity, Hölder continuous, Perron solution, $p$-harmonic, Sobolev extension, Whitney covering

MSC Classifications:

46E35, 31C45 show english descriptions Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems
Other generalizations (nonlinear potential theory, etc.) 46E35 - Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems
31C45 - Other generalizations (nonlinear potential theory, etc.)

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