Riemann–Hilbert problem in the class of Cauchy type integrals with densities of grand Lebesgue Spaces

Abstract

The present paper deals with a solution of the Riemann–Hilbert problem with piecewise continuous coefficients in the class of Cauchy type integrals with densities in grand Lebesgue spaces. Necessary and sufficient solvability condition is established. In solvability case the solutions in explicit form are constructed.

Keywords:

• Riemann–Hilbert problem
• Cauchy type integrals
• Cauchy singular integral
• grand Lebesgue spaces
• weights

AMS Subject Classifications:

• Primary: 47B35
• 30E20
• 47P95
• Secondary: 47B38
• 30E25

Acknowledgements

The authors would like to thank the anonymous reviewers for their helpful and valuable comments and suggestions.

Notes

No potential conflict of interest was reported by the authors.