Sharp weak-type estimate for local lifted Hardy–Littlewood maximal operators with applications to generators of linear operator families and Hardy(–Sobolev) spaces

Key Points

• Sharp weak-type estimates are crucial for understanding local lifted operators in various mathematical contexts.
• The study presents significant implications for the generators of linear operator families under the framework of Hardy spaces.
• Assessment of these maximal operators involves advanced techniques in functional analysis and operator theory.
• Findings highlight the importance of these estimates in expanding the applications of Hardy and Sobolev spaces.