New characterizations of BLO spaces by heat semigroups and applications

TL;DR

This paper introduces two novel characterizations of BLO spaces using heat semigroups, demonstrating their applications in analyzing heat equation solutions and revisiting BMO-BLO boundedness of Littlewood-Paley g-function.

Contribution

It provides new characterizations of BLO spaces via heat semigroups and applies these to heat equation regularity and BMO-BLO boundedness proofs.

Findings

New characterizations of BLO spaces using Gaussian heat semigroup

Proved regularity of heat equation solutions with BLO boundary conditions

Reproved BMO-BLO boundedness of Littlewood-Paley g-function

Abstract

In this paper, we give two new characterizations of the bounded lower oscillation(BLO) space by using the Gaussian heat semigroup. By the new characterizations, we prove the regularity property of the solutions to the heat equation with BLO boundary value. Also, we reprove the BMO-BLO boundedness of the Littlewood-Paley $g$-function by using the semigroup method.