Rearrangement invariant envelopes of generalized Besov, Sobolev, and Calderon spaces

We give a survey of some recent results concerning the description of the rearrangement invariant envelopes of the generalized Besov, Sobolev, and Calderon spaces. We describe the smallest rearrangement invariant spaces in which these spaces are embedded. These results are based on equivalent descriptions of the cones of decreasing rearrangements for functions in Besov, Sobolev or Calderon spaces.