Abstract:
An estimate $ p^{\frac1p}q^{\frac1q}{\leqslant}\lambda_p$ of $\mathscr{K}$-divisibility constant has been obtained for
a pair of weighted $L_p$ spaces.
In view of the known estimate for $\mathscr{K}$-divisibility constant
for an arbitrary pair of Banach lattices this implies that ${2\leqslant}\lambda{\leqslant}4$.
Key words:Banach couple, interpolation of linear operators, $\mathscr{K}$-functional, $\mathscr{K}$-method, constant $\mathscr{K}$-divisibility.
Fulltext:
PDF file (109 kB)