The sharpness of the classical first order Orlicz Sobolev imbedding theorem is discussed in the case in which the Orlicz function increases essentially more slowly than a power function

We give equivalent conditions for tensor product of Orlicz sequence spaces, then we obtain a necessary and sufficient condition for a class of matrix operators acting on Orlicz sequence spaces to be continuous and compact.

We consider the approximation by linear finite elements of the solution of the Dirichlet problem -Au = /. We obtain a relation between the error in the infinite norm and the error in some Orlicz spaces. As a consequence, we get quasi-optimal uniform estimates when u has second derivatives in the Orlicz space associated with the exponential function. This estimate contains, in particular, the ca...

Using recent characterizations of the compactness of composition operators on HardyOrlicz and Bergman-Orlicz spaces on the ball ([2, 3]), we first show that a composition operator which is compact on every Hardy-Orlicz (or Bergman-Orlicz) space has to be compact on H∞. Then, although it is well-known that a map whose range is contained in some nice Korányi approach region induces a compact comp...