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

Bilalov B., Ahmedzade N., Kasumov Z.

Lobachevskii Journal of Mathematics, cilt.46, sa.1, ss.377-387, 2025 (ESCI) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 46 Sayı: 1
  • Basım Tarihi: 2025
  • Doi Numarası: 10.1134/s1995080224608129
  • Dergi Adı: Lobachevskii Journal of Mathematics
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, zbMATH
  • Sayfa Sayıları: ss.377-387
  • Anahtar Kelimeler: Dirichlet problem, harmonic functions, Muckenhoupt class, weighted grand Lebesgue space
  • Yıldız Teknik Üniversitesi Adresli: Hayır

Özet

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.