Extensions of the Hardy-Littlewood inequalities for Schwarz symmetrization - H. Hajaiej; C. A. Stuart (International Journal of Mathematics and Mathematical Sciences)
For a class of functions H:(0,∞)×ℝ+2→ℝ, including discontinuous functions of Carathéodory type, we establish that ∫ℝNH(|x|,u(x),v(x))dx≤∫ℝNH(|x|,u*(x),v*(x))dx, where u*(x) and v*(x) denote the Schwarz symmetrizations of nonnegative functions u and v.