The Weighted Grand Lebesgue Class of Harmonic Functions and the Dirichlet Problem

Bilalov B., Ahmedzade N., Kasumov Z.

Lobachevskii Journal of Mathematics, vol.46, no.1, pp.377-387, 2025 (ESCI, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 46 Issue: 1
  • Publication Date: 2025
  • Doi Number: 10.1134/s1995080224608129
  • Journal Name: Lobachevskii Journal of Mathematics
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, zbMATH
  • Page Numbers: pp.377-387
  • Keywords: Dirichlet problem, harmonic functions, Muckenhoupt class, weighted grand Lebesgue space
  • Yıldız Technical University Affiliated: No

Abstract

Abstract: In this paper, we introduce the weighted grand Lebesgue class of harmonic function in unit ball on the complex plane. It is established some properties of functions from theseclasses, when the weight function satisfy the Muckenhoupt condition. It is proved the unique solvability of theDirichlet problem for Laplace equation with an arbitrary boundaryvalue from weighted grand Lebesgue space on.