Best constants in reverse Riesz-type inequalities for analytic and co-analytic projections

{abstract} Let P₊ be the Riesz's projection operator and let P₋= I - P₊. We consider the inequalities of the following form \|f\|Lᵖ(T)≤ Bp,s\|( |P_ + f | ˢ + |P₋ f |ˢ) ¹ˢ\|Lᵖ (T) and prove them with sharp constant Bp,s for s ∈ [p',+∞) and 1<p≤ 2 and p≥ 9, where p':=min,p/p-1\. {abstract}