The necessary and sufficient conditions are found for the weight function v, which provide the boundedness and compactness of the Riemann–Liouville operator Rα from Lp to L q v . The criteria are also established for the weight function w, which guarantee the boundedness and compactness of the Weyl operator Wα from L p w to Lq . In this paper, the necessary and sufficient conditions are found f...

The problem of characterizing conformally Einstein manifolds by tensorial conditions has been tackled recently in papers by M. Listing, and in work by A. R. Gover and P. Nurowski. Their results apply to metrics satisfying a " non-degeneracy " condition on the Weyl tensor W. We investigate the geometry of the foliations arising on conformally Einstein spaces (with Riemannian signature) where thi...

Weyl denominator identity for the affinization of a basic Lie superalgebra with non-zero Killing form was formulated by V. Kac and M. Wakimoto and was proven by them for the defect one case. In this paper we prove this identity. 0. Introduction Let g be a basic Lie superalgebra with a non-zero Killing form. Let ĝ be the affinization of g. Let h (resp., ĥ) be the Cartan subalgebra in g (resp., i...

We use the author's combinatorial theory of full heaps to categorify the action of a large class of Weyl groups on their root systems, and thus to give an elementary and uniform construction of a family of faithful permutation representations of Weyl groups. Examples include the standard representations of affine Weyl groups as permutations of Z and geometrical examples such as the realization ...

We use the author's combinatorial theory of full heaps to categorify the action of a large class of Weyl groups on their root systems, and thus to give an elementary and uniform construction of a family of faithful permutation representations of Weyl groups. Examples include the standard representations of affine Weyl groups as permutations of Z and geometrical examples such as the realization ...

A homogeneous fractional-differential equation with a fractional Hardy—Titchmarsh integral and an unbounded operator coefficient in Banach space is considered. The conditions for the representation of solution form Danford—Cauchy are established, exponentially convergent approximation method developed.