Sharp estimates for martingale transforms with unbounded transforming sequences
Sharp estimates for martingale transforms with unbounded transforming sequences
Suppose that p,q,r≥1 satisfy the condition 1 p=1 q+1 r. The paper contains the identification of the best constants cp,q,r and Cp,q,r in the estimates ‖g‖p,∞≤cp,q,r‖f‖q‖v∗‖ r,‖g‖p≤Cp,q,r‖f‖q‖v∗‖ r where f is an arbitrary Hilbert-space valued martingale, g is its transform by a predictable sequence v, and v∗ is the maximal …