In this note, we investigate the relation between double points and complex points of immersed surfaces in almost–complex 4–manifolds and show how estimates for the minimal genus of embedded surfaces lead to inequalities between the number of double points and the number of complex points of an immersion. We also provide a generalization of a classical genus estimate due to V.A. Rokhlin to the ...

David and Journé discovered a criterion for the continuity on L of CalderónZygmund operators defined by singular integrals. In their approach the distributional kernel of the given operator is locally Hölder continuous outside the diagonal. The aim of this paper is to prove a David-Journé theorem where this smoothness assumption is replaced by a weaker one. Our approach strongly relies on an al...

The story of the friendship and collaboration between Vladimir Abramovich Rokhlin Nizhny Novgorod mathematician Dmitry Andreevich Gudkov during last period Rokhlin’s mathematical biography, when he worked in topology real algebraic varieties, which obtained remarkable results. paper is based on correspondence 1971–1982 preserved Gudkov’s archive containing 15 letters by V. A.Rokhlin 8 D. A. Gud...