Hardy—Littlewood—Sobolev Inequalities with the Fractional Poisson Kernel and Their Applications in PDEs
| Autor: | Lu Chen, Chunxia Tao, Guozhen Lu |
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| Rok vydání: | 2019 |
| Předmět: | |
| Zdroj: | Acta Mathematica Sinica, English Series. 35:853-875 |
| ISSN: | 1439-7617 1439-8516 |
| Popis: | The purpose of this paper is five-fold. First, we employ the harmonic analysis techniques to establish the following Hardy-Littlewood-Sobolev inequality with the fractional Poisson kernel on the upper half space $$\int_{\mathbb{R}_ + ^n} {{{\int_{\partial \mathbb{R}_ + ^n} {f\left( \xi \right)P\left( {x,\xi,\alpha } \right)g\left( x \right)d\xi dx \leq {C_{n,\alpha,p,q'}}\parallel g\parallel } }_{Lq'\left( {\mathbb{R}_ + ^n} \right)}}} \parallel f{\parallel _{Lq'\left( {\partial \mathbb{R}_ + ^n} \right),}}$$ where $$f\, \in \,{L^p}\left( {\partial \mathbb{R}_ + ^n} \right),\,g\, \in \,{L^{q'}}\left( {\mathbb{R}_ + ^n}\right)\,\text{and}\;\,p,\,q'\, \in \,\left( {1 + \infty } \right),\,2\, \leq {\alpha |
| Databáze: | OpenAIRE |
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