Boundedness criteria for singular integrals in weighted grand lebesgue spaces

Boundedness criteria for the Calderón singular integral, Riesz transform and Cauchy singular integral in generalized weighted grand Lebesgue spaces L ^p),θ _w , 1 < p < ∞, are studied. It is shown that an operator K of this type is bounded in L ^p),θ _w if and only if the weight w satisfies the Muckenhoupt A _p condition. Bibliography: 15 titles.