Alexandru D. IonescuUniversity of Wisconsin, Madison, Madison, WI, U.S.A.Elias M. SteinPrinceton University, Princeton, NJ, U.S.A.Akos MagyarUniversity of Georgia, Athens, Athens, GA, U.S.A.Stephen WaingerUniversity of Wisconsin, Madison, Madison, WI, U.S.A.
We prove$L$^{$p$}boundedness of certain non-translation-invariant discrete maximal Radon transforms and discrete singular Radon transforms. We also prove maximal, pointwise, and$L$^{$p$}ergodic theorems for certain families of non-commuting operators.
B. HelfferPlateau de Palaiseau, Centre de Mathématiques de l'Ecole PolytechniqueJ. F. NourrigatDépartement de Mathématiques et Informatique, BP 25A, Rennes Cedex, France
We determine the smallest Schatten class containing all integral operators with kernels in$L$_{p}(L_{p', q})^{symm}, where 2 <$p$∞ and 1≦$q$≦∞. In particular, we give a negative answer to a problem posed by Arazy, Fisher, Janson and Peetre in [1].