Improved Muckenhoupt-Wheeden inequality and weighted inequalities for potential operators

By a variant of the standard good $\lambda$ inequality, we prove the Muckenhoupt-Wheeden inequality for measures which are not necessarily in the Muckenhoupt class. Moreover we can deal with a general potential operator, and consequently we obtain a suitable approach to the two weight inequality for such an operator when one of the weight functions satisfies a reverse doubling condition.