Approximation and transfer of properties between net-type and translation invariant convex differentiation bases
Tom 176 / 2024
Streszczenie
Let be a net-type convex differentation basis and \mathbf H be a translation invariant convex differentation basis. We show the transfer of differentiation properties for non-negative functions from \mathbf B to \mathbf H provided \mathbf B is a subbasis of some translation invariant density basis and each set H forming \mathbf H can be approximated by some set B forming \mathbf B in the sense that | B\triangle H|\leq c | B\cap H|, where c is a positive constant not depending on H. Some applications for net-type bases formed by rectangles with dyadic type constraints are given.