In the present work the space  $L_{p;r} $ which is continuously embedded into $L_{p} $  is introduced. The corresponding Hardy spaces of analytic functions are defined as well. Some properties of the functions from these spaces are studied. The analogs of some results in the classical theory of Hardy spaces are proved for the new spaces. It is shown that the Cauchy singular integral operator is...

1.1. This is the first of two papers addressing a Cauchy type inequality for the geometric intersection number between two 1-dimensional submanifolds in a surface. As a consequence, we reestablish some of the basic results in Thurston's theory of measured laminations. In this paper, we consider surfaces with non-empty boundary using ideal triangulations. In the sequel, we establish the inequali...

We study different completeness definitions for two categories of lattice-valued Cauchy spaces and the relations between these definitions. We also show the equivalence of a so-called completion axiom and the existence of a completion.

It is shown that the only vacuum algebraically special space-time that is asymptotically simple is Minkowski space. The structure of null infinity for algebraically special space-times satisfying a subset of the vacuum equations is shown to be particularly simple in terms of the coordinates used in Kerr's original reduction of the field equations. With the assumption of the existence of a globa...

n this paper, we apply picard’s iteration method followed by adomian decomposition method to solve a nonlinear singular cauchy problem of euler- poisson- darboux equation. the solution of the problem is much simplified and shorter to arriving at the solution as compared to the technique applied by carroll and showalter (1976)in the solution of singular cauchy problem.