Sharp Hardy–Littlewood–Sobolev Inequality on the Upper Half Space
Sharp Hardy–Littlewood–Sobolev Inequality on the Upper Half Space
The sharp Hardy–Littlewood–Sobolev inequality on the upper half space is proved. The existences of extremal functions are obtained. For certain exponent, we classify all extremal functions via the method of moving sphere, and compute the best constants for the sharp inequality.