Boundary conjugation problem for piecewise analytic functions in Besov spaces

Abstract

The main aim of this work is to show the solvability of the homogeneous and inhomogeneous boundary conjugation problems for piecewise analytic functions in the Besov space, which is embedded into the class of continuous functions.

Keywords:

• Boundary value conjugation problems
• piecewise-analytic functions
• Cauchy type integrals
• Besov spaces

AMS Subject Classifications:

• 46E30
• 47B10
• 46L51
• 46L52
• 44A15
• Secondary 47L20
• 47C15

Acknowledgments

We thank the anonymous referee for reading the paper carefully and providing thoughtful comments, which improved the exposition of the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was partially supported by Grant No. AP19677346 of the Science Committee of the Ministry of Science and Higher Education of the Republic of Kazakhstan.