I've stumbled upon a problem involving the trace of a function in a fractional Sobolev space of the form W^{s,2}(H), where H is a half-plane in R^2. Would it be possible to define a notion of trace, in the case in which 0<s<1/2? If yes, is there a characterization of the space of such traces? Are the traces locally integrable? Are you aware of any reference where such information could be found?