ABSTRACT
This survey, incomplete as it may be, deals with some of the recent results on limiting imbeddings of Sobolev spaces and their generalizations. Several particular topics will be dealt with in next sections: first we recall definitions of function spaces in the framework of the Fourier analysis approach, we tackle particular extrapolation procedures for Lebesgue and Holder spaces, and then we come to the core, considering spaces with dominating mixed derivatives (in particular then the reduced Sobolev spaces) and their limiting imbed dings. We shall mostly omit the proofs since they are technically rather complicated. In this case the references for details are [18] and [19]. Nevertheless, in the cases when we have found short and relatively simple proofs of some claims both on limiting imbeddings and extrapolation, we include them.
