Exponential and moment inequalities for U-statistics
  A Bernstein-type exponential inequality for (generalized) canonical U-statistics of order 2 is obtained and the Rosenthal and Hoffmann-J{\o}rgensen inequalities for sums of independent random variables are extended to (generalized) U-statistics of any order whose kernels are either nonnegative or canonical 
Evarist Gin\'e (University of Connecticut), Rafa{\l} Lata{\l}a (Warsaw   University), and Joel Zinn (Texas A&M University)