The analysis of orthogonal polynomials associated with general weights has been a major theme in classical analysis this century. The use of potential theory since the early 1980 s had a dramatic influence on the development of orthogonal polynomials associated with weights on the real line. For many applications of orthogonal polynomials, for example in approximation theory and numerical analysis, it is not asymptotics but certain bounds that are most important. In this monograph, the authors define and discuss their classes of weights, state several of their results on Christoffel...