On Riemann problem in weighted Smirnov classes with general weight

  • Bilal Bilalov Institute of Mathematics and Mechanics of NAS of Azerbaijan
  • Aysel Guliyeva Ganja State University
  • Sabina Sadigova Institute of Mathematics and Mechanics of NAS of Azerbaijan
Keywords: weighted Smirnov classes, Riemann problem, Muchkenhoupt condition

Abstract

Weighted Smirnov classes in bounded and unbounded domains are defined in this work. Nonhomogeneous Riemann problems with a measurable coefficient whose argument is a piecewise continuous function are considered in these classes. A Muckenhoupt type condition is imposed on the weight function and the orthogonality condition is found for the solvability of nonhomogeneous problem in weighted Smirnov classes, and the formula for the index of the problem is derived. Some special cases with power type weight function are also considered,
and conditions on degeneration order are found.

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Published
2021-06-21
Section
Articles