Weighted estimates for singular integrals and their applications

We give a survey of research on the problem of single-weighted and double-weighted estimates of strong and weak types for the Hardy–Littlewood maximal function, Riesz potentials, singular integral operators, and harmonic functions. Necessary and sufficient conditions on the weight are given under which weighted estimates are valid (Muckenhoupt's $A_p$-condition, Sawyer's condition, etc.). Special attention is given to papers which appeared after 1980 and the latest results, published as reports and preprints.