Hardy-Littlewood majorants in function spaces

Some remarks on multilinear maps and interpolation

“…For instance the Hardy-Littlewood maximal operator is bounded on X (r.i. over R n ) if and only if q X < ∞, see [13], [18]. The Hilbert transform is bounded on X (r.i. over R) if and only if 1 < p X ≤ q X < ∞, see [2].…”

On some martingale inequalities for mean oscillations in weak spaces

“…Then the boundedness of P and Q on Z can be characterized by the values of the Boyd indices of Z ; Shimogaki [10] proved implicitly that…”

On certain martingale inequalities for maximal functions and mean oscillations

“…Then β X < 1 if and only if P ∈ B( X), and α X > 0 if and only if Q ∈ B( X) (see [1,Theorem 5.15, p. 150]; cf. [10]). …”