K-closedness of weighted Hardy spaces on the two-dimensional torus

TL;DR

This paper investigates the K-closedness property of weighted Hardy spaces on the two-dimensional torus, extending previous results to include certain nonsplit weights under specific restrictions.

Contribution

It introduces new conditions under which weighted Hardy spaces with nonsplit weights are K-closed in weighted Lebesgue spaces on the two-dimensional torus.

Findings

K-closedness established for certain nonsplit weights

Extends previous results beyond split weights

Provides conditions for weighted Hardy spaces on the torus

Abstract

It is proved that, under certain restrictions on weights, a pair of weighted Hardy spaces on the two-dimensional torus is K-closed in the pair of the corresponding weighted Lebesgue spaces. By now, K-closedness of Hardy spaces on the two-dimensional torus was considered either in the case of no weights or in the case of weights that split into a product of two functions of one variable (the so-called "split weights"). Here the case of certain nonsplit weights is studied.