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We introduce and study the classes Pp (Rn) as well as Pp (Rn) , which are generalization of the Kato class. We also obtain a Fefferman inequality for the class Pp (Rn) and derive the weak Harnack inequality. Mathematics subject classification (2010): Primary 46E35; Secondary 31B10, 35A32, 39B72.

Weak Harnack inequality for the non-negative weak supersolution of quasilinear elliptic equation