The Calderón’s Construction for Pairs of Grand and Small Lebesque Spaces

We find conditions under which the Calderón construction for a pair of Grand or Small Lebesque spaces is also Grand or Small Lebesque spaces. Based on the well-known reduction, the calculation of the Calderón construction for pairs of Grand and Small Lebesque spaces allowed us to describe the spaces of the complex interpolation method for these pairs of spaces and to obtain new interpolation theorems for Grand and Small Lebesque spaces.