The Riesz “rising sun” lemma for arbitrary Borel measures with some applications - Lasha Ephremidze; Nobuhiko Fujii; Yutaka Terasawa (Journal of Function Spaces and Applications)
The Riesz “rising sun” lemma is proved for arbitrary locally finite Borel measures on the real line. The result is applied to study an attainability problem of the exact constant in a weak (1,1) type inequality for the corresponding Hardy-Littlewood maximal operator.