Sparse and non–Euclidean extensions of weak–type estimates

Abstract

We develop new extensions of classical weighted weak–type inequalities by incorporating recent advances in sparse domination, non–Euclidean and non–doubling settings, and vector-valued analysis. Our approach provides quantitative bounds that capture the dependence on weight characteristics, and we illustrate applications to time–frequency analysis and pseudodifferential operators. In addition, we establish novel duality and interpolation results, offering a comprehensive framework that extends the reach of weak–type estimates in harmonic analysis.