A general approach to weighted Rellich type inequalities on Carnot groups

Goldstein J. A., KÖMBE İ., YENER A.

Monatshefte fur Mathematik, cilt.186, sa.1, ss.49-72, 2018 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 186 Sayı: 1
  • Basım Tarihi: 2018
  • Doi Numarası: 10.1007/s00605-017-1060-z
  • Dergi Adı: Monatshefte fur Mathematik
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.49-72
  • Anahtar Kelimeler: Carnot groups, Weighted Rellich inequality, Remainder term
  • İstanbul Ticaret Üniversitesi Adresli: Evet

Özet

We give a simple sufficient criterion on a pair of nonnegative weight functions a and b on a Carnot group G, so that the following general weighted Lp Rellich type inequality∫Ga|ΔGu|pdx≥∫Gb|u|pdxholds for every u∈C0∞(G) and p> 1. It is worthwhile to notice that our method easily derives previously known weighted Rellich type inequalities with a sharp constant in a more adequate fashion and also enables us to obtain new ones. We also present a sharp Lp Rellich type inequality that connects first to second order derivatives and some new two-weight Rellich type inequalities with remainders on bounded domains Ω in G via a differential inequality and the improved two-weight Hardy inequality in Goldstein et al. (Discret Contin Dyn Syst 37:2009–2021, 2017).