Abstract:

HardyLittlewoodSobolev (HLS) inequality and the Wolff inequality were used to obtain the L^p estimate of the Wolff potentials. At the same time,  EulerLagrange equations of the extremal functions for the more general weighted HLS inequalities were also established by means of the method of calculus of variations.

Key words: HardyLittlewoodSobolev inequality, Wolff potential, calculus of variations, fractional order partial differential equations (PDEs)