Hardy and rellich type inequalities with two weight functions

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Ahmetolan S., KÖMBE İ.

Mathematical Inequalities and Applications, cilt.19, sa.3, ss.937-948, 2016 (SCI-Expanded, Scopus)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 19 Sayı: 3
  • Basım Tarihi: 2016
  • Doi Numarası: 10.7153/mia-19-68
  • Dergi Adı: Mathematical Inequalities and Applications
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.937-948
  • Anahtar Kelimeler: Hardy inequality with two weight functions, Rellich inequality with two weight functions, sharp constant
  • Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
  • İstanbul Ticaret Üniversitesi Adresli: Evet

Özet

In the present paper we prove several sharp two-weight Hardy, Hardy-Poincaŕe, and Rellich type inequalities on the sub-Riemannian manifold R2n+1 = Rn x Rn xR defined by the vector fields: Xj = ∂ /∂ xj +2kyj |z|2k?2 ∂/ ∂ l Yj = ∂ /∂ yj ?2kxj |z|2k?2∂/ ∂ l, j = 1,2, ..,n where (z,y) = (x,y, l) ∂ R2n+1 , |z| = (|x|2 +|y|2)1/2 and k ≥ 1.