Existence of an extremal of Dunkl-type Sobolev inequality and of Stein-Weiss inequality for D-Riesz potential

Existence of an extremal of Dunkl-type Sobolev inequality and of Stein-Weiss inequality for D-Riesz potential

In this paper, we prove the existence of an extremal for the Dunkl-type Sobolev inequality in case of \(p=2\). Also we prove the existence of an extremal of the Stein-Weiss inequality for the D-Riesz potential in case of \(r=2\).

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Veröffentlicht in:arXiv.org 2019-05
Hauptverfasser: Adhikari, Saswata, Anoop, V P, Parui, Sanjay
Format: Artikel
Sprache:eng
Schlagworte:
Inequality
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Zusammenfassung:In this paper, we prove the existence of an extremal for the Dunkl-type Sobolev inequality in case of \(p=2\). Also we prove the existence of an extremal of the Stein-Weiss inequality for the D-Riesz potential in case of \(r=2\).
ISSN:2331-8422