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Existence of Extremals of Dunkl-Type Sobolev Inequality and of Stein–Weiss Inequality for Dunkl Riesz Potential
Complex Analysis and Operator Theory ( IF 0.7 ) Pub Date : 2021-01-27 , DOI: 10.1007/s11785-020-01068-1 Saswata Adhikari , V. P. Anoop , Sanjay Parui
中文翻译：
Dunkl Riesz势的Dunkl型Sobolev不等式和Stein-Weiss不等式的极值的存在
更新日期：2021-01-28
Complex Analysis and Operator Theory ( IF 0.7 ) Pub Date : 2021-01-27 , DOI: 10.1007/s11785-020-01068-1 Saswata Adhikari , V. P. Anoop , Sanjay Parui
In this paper, we prove the existence of an extremal for the Dunkl-type Sobolev inequality in the case of \(p=2\). Also we prove the existence of an extremal of the Stein–Weiss inequality for the Dunkl Riesz potential in the case of \(r=2\).
中文翻译：
Dunkl Riesz势的Dunkl型Sobolev不等式和Stein-Weiss不等式的极值的存在
在本文中，我们证明了在\（p = 2 \）的情况下Dunkl型Sobolev不等式存在极值。同样，在\（r = 2 \）的情况下，我们证明了Dunkl Riesz势的Stein-Weiss不等式的极值。
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