English

A regularity theory for an initial value problem with a time-measurable pseudo-differential operator in a weighted $L_p$-space

Analysis of PDEs 2025-10-22 v4

Abstract

In this study, we investigate the existence, uniqueness, and maximal regularity estimates of solutions to homogeneous initial value problems involving time-measurable pseudo-differential operators within the framework of weighted mixed norm Lebesgue spaces. The class of temporal weights in our regularity estimates contains Muckenhoupt's class, and the initial data is in weighted Besov spaces with variable order.

Keywords

Cite

@article{arxiv.2302.07507,
  title  = {A regularity theory for an initial value problem with a time-measurable pseudo-differential operator in a weighted $L_p$-space},
  author = {Jae-Hwan Choi and Ildoo Kim and Jin Bong Lee},
  journal= {arXiv preprint arXiv:2302.07507},
  year   = {2025}
}

Comments

47 pages; The paper has been accepted for publication in "Potential Analysis"

R2 v1 2026-06-28T08:40:30.421Z