Necessary and Sufficient Conditions for Weighted Boundedness of Integral Transforms Defined on Product Spaces in Generalized Grand Lebesgue Spaces

摘要

The paper deals with one-weighted boundedness criteria for the integral transforms generated by the strong maximal functions, multiple conjugate functions and Hilbert transforms in grand Lebesgue spaces with respect to measurable functions. We characterize both weak and strong type weighted inequalities. Both cases of weighted spaces differing by position of the weight function in the norms are explored.