We study the existence of solutions mixed Riemann-Hilbert or Cherepanov boundary value problem with simply connected fibers on unit disk Δ. Let L be a closed arc ∂Δ end points ω−1,ω1 and let smooth function no zeros. {γξ}ξ∈∂Δ∖L˚ family Jordan curves in C which all contain point 0 their interiors such that γω−1, γω1 are strongly starshaped respect to 0. Then under condition for each w∈γω±1 angle...

The Bogomolny equations for Yang-Mills-Higgs monopoles follow from a system of linear equations which may be solved through a parametric Riemann-Hilbert problem. We extend this approach to noncommutative R and use it to (re)construct noncommutative Dirac, Wu-Yang, and BPS monopole configurations in a unified manner. In all cases we write down the underlying matrix-valued functions for multi-mon...

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...