Abstract
This work establishes necessary and sufficient conditions for the boundedness of one variable differential operator acting from a weighted Sobolev space W^l_p,v to a weighted Lebesgue space on the positive real half line. The coefficients of differential operators are often assumed to be pointwise multipliers of function spaces. The author introduces pointwise multipliers in weighted Sobolev spaces; obtains the description of the space of multipliers M(W_1 → W_2) for a pair of weighted Sobolev spaces (W_1, W_2) with weights of general type.