Self-improving properties of a generalized Muckenhoupt class.

We first prove some new weighted refinements of inequalities of Hardy's type with negative powers. Next, we prove that any A λ 1 Muckenhoupt class with a weight λ belongs to some weighted Gehring class G λ p for p > 1 . We also prove that the self-improving property of the weighted Muckenhoupt class A λ q holds. The main results give exact values of the limit exponents and the constants of the new classes. The self-improving property of the weighted Muckenhoupt class will then be applied to prove the self-improving property of the Gehring class with a sharp value on the exponents. [ABSTRACT FROM AUTHOR]