Аннотация
Let and be a pair of Banach spaces of functions in . A multiplier from into is a function on such that . By the norm one means the norm of the operator , . Conditions ensuring that a function belongs to the multiplier classes and are found, where and are Sobolev and Lebesgue weighted spaces, respectively. Estimates of the norms of multipliers free from capacity characteristics are found. Special local maximal operators are introduced and significantly used.