Abstract:
It is well known that functions from Hardy classes have limit values almost everywhere on the boundary.
For example, in the case of the unit circle, it is the nontangent limits that are optimal
and cannot be replaced by any tangent areas. We consider the problem of the existence of limit values that take into account all values of a function from small neighborhoods of points on the boundary. This problem is studied within the framework of some abstract version of Hardy-type classes. The tools used to solve the problem will also be described: a modification of the Marcinkiewicz interpolation theorem for Hardy-type spaces and generalized Hardy-Littlewood inequalities.