Sharp Weak-Type (p, p) Estimates ($$1<p<\infty $$) for Positive Dyadic Shifts

Abstract

The paper contains the study of sharp weak-type estimates for positive dyadic shifts on $${\mathbb {R}}^d$$ . The proof exploits Bellman function method: the inequalities are deduced from the existence of certain associated special functions, enjoying appropriate majorization and concavity conditions.