General weighted hardy type inequalities related to Baouendi-Grushin operators
Complex Variables and Elliptic Equations, cilt.63, sa.3, ss.420-436, 2018 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 63 Sayı: 3
- Basım Tarihi: 2018
- Doi Numarası: 10.1080/17476933.2017.1318128
- Dergi Adı: Complex Variables and Elliptic Equations
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.420-436
- Anahtar Kelimeler: Baouendi-Grushin vector fields, weighted Hardy inequality, Heisenberg-Pauli-Weyl inequality, two-weight Hardy inequality, remainder terms
- İstanbul Ticaret Üniversitesi Adresli: Evet
Özet
In this paper, we derive a sufficient condition on a pair of nonnegative weight functions ϑ and w in ℝm+k so that the general weighted Hardy type inequality with a remainder term (Formula Presented) is the sub-elliptic gradient. It is worth emphasizing here that our unifying method may be readily used to recover most of the previously known sharp weighted Hardy and Heisenberg-Pauli-Weyl type inequalities as well as to construct other new inequalities with an explicit constant. Furthermore, we also obtain new results on two-weight Lp Hardy type inequalities with remainder terms on smooth bounded domains Ω in ℝm+k via a non-linear partial differential inequality.