In the present paper we have studied an N(k)-quasi Einstein manifold satisfying R(ξ, X).P̃ , where P̃ is the pseudo-projective curvature tensor. Among others, it is shown that if quasi-Einstein manifold with constant associated scalars is Ricci symmetric then the generator of the manifold is a Killing vector field. AMS Mathematics Subject Classification (2000): 53C25

We consider the Cauchy problem periodic in the spatial variable for the usual cubic nonlinear Schrödinger equation and construct an infinite sequence of invariant measures associated with higher conservation laws for dynamical systems generated by this problem on appropriate phase spaces. In addition, we obtain sufficient conditions for the boundedness of the measures constructed. 2000 Mathemat...

We consider some reaction-diffusion equations perturbed by white noise and prove Schauder estimates for the elliptic problem associated with the generator of the corresponding transition semigroup, defined in the Banach space of continuous functions. This requires the proof of some new interpolation result. 2000 Mathematics Subject Classification AMS: 35R15, 60H15, 35B45

In this paper we use the resolvent semigroup associated to a C0semigroup to introduce the vector-valued Stieltjes transform defined by a C0-semigroup. We give new results which extend known ones in the case of scalar generalized Stieltjes transform. We work with the vector-valued Weyl fractional calculus to present a deep connection between both concepts. Mathematics Subject Classification (200...

We completely classify type III factor representations of CuntzKrieger algebras associated with quasi-free states up to unitary equivalence. Furthermore, we realize these representations on concrete Hilbert spaces without using GNS construction. Free groups and their type II1 factor representations are used in these realizations. Mathematics Subject Classification (2000). 46K10, 46L30.

We prove an existence result for the Dirichlet problem associated to some degenerate quasilinear elliptic equations in a bounded open set Ω in R in the setting of weighted Sobolev spaces W 1,p 0 (Ω, ω). 2000 Mathematics Subject Classification: 35J70, 35J60.

We define a multidimensional rearrangement, which is related to classical inequalities for functions that are monotone in each variable. We prove the main measure theoretical results of the new theory and characterize the functional properties of the associated weighted Lorentz spaces. Mathematics Subject Classification 2000: 46E30, 46B25.

The main purpose of the present paper is to investigate some subordination-preserving and superordination-preserving properties of a certain family of integral operators. Several sandwich-type results associated with this family of integral operators are also derived. 2000 Mathematics Subject Classification. Primary 30C45; Secondary 30C80.

We describe a generalisation of the FontaineWintenberger theory of the “field of norms” functor to local fields with imperfect residue field, generalising work of Abrashkin for higher dimensional local fields. We also compute the cohomology of associated p-adic Galois representations using (φ,Γ)-modules. 2000 Mathematics Subject Classification: 11S15, 11S23, 11S25, 12G05

We show that for every nontrivial potential space LK(R n), there exists an approach region for which the associated maximal function is of weak-type, but the boundedness for the completed region is false, which is in contrast with the nontangential case. Mathematics Subject Classification 2000: 42B25, 42B20.