Interpolation of classical Lorentz spaces measuring oscillation
arXiv:2512.23287
Abstract
We obtain an explicit characterization of the -functional of a pair of weighted classical Lorentz spaces of type . We develop a method for obtaining such characterization based on a relation between the desired quantity and the -functional of a specific couple of spaces of type , which are substantially more manageable than their companions of type . The core of our techniques is a subtle manipulation with respective fundamental functions. We present several applications, in particular we nail down a formula for the -functional of a Lebesgue space and a classical Lorentz space of type with a power weight, and using this formula we establish an inequality of a reverse Marchaud type.
27 pages, 0 figures