We prove two pointwise estimates relating some classical maximal and singular integral operators. In particular, these estimates imply well-known rearrangement inequalities, and BLO-norm inequalities
We derive weighted rearrangement estimates for a large class of area integrals. The main approach used earlier to study these questions is based on distribution function inequalities.
We investigate the classical embedding . The sharp asymptotic behaviour as s → 1 of the operator norm of this embedding is found. In particular, our result yields a refinement of the Bourgain, Brezis and Mironescu theorem concerning an analogous problem for the Sobolev-type embedding. We also give a different, elementary proof of the latter theorem.
A scale of function spaces is considered which proved to be of considerable importance in analysis. Interpolation properties of these spaces are studied by means of the real interpolation method. The main result consists in demonstrating that this scale is interpolated in a way different from that for Lp spaces, namely, the interpolation space is not from this scale.
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