On the uniqueness of the reconstruction of a function summable in a strip defined by integrals along the arcs of one two-parameter family of hyperbolas

The uniqueness of the reconstruction of integrable in the strip in the plane functions, given its integrals along the arcs of the two-parameter family of hyperbole with weight, analytical by part of the variables is proved.
The method of proof is based on the construction majorant of first kind operator of Volterra for the operator in scales of Banach spaces.