On Tangential Boundary Behavior of Functions from Hardy Type Spaces

It is well known that functions from the Hardy spaces have limit values almost everywhere on the boundary. For example, in case of the unit circle, these are limits by nontangential domains. These nontangential domains are optimal and cannot be replaced by any tangent domains.

Within the framework of some abstract version of Hardy-type spaces, we study the question of the existence of limits that takes into account all values of a function from small neighborhoods of boundary points.

We also describe the tools used to study the problem, such as a modification of the diagonal Marcinkiewicz interpolation theorem for spaces of Hardy type and generalized Hardy–Littlewood inequalities.