On Maximal L^p-regularity

2009/02/16 by Frédéric Bernicot, Bernicot, Frédéric, Jiman Zhao +1
Mathematics · #42B25 #42B30 #42B35 #46M35 #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.0902.2691

openalex publication_date 2009/02/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The aim of this paper is to propose weak assumptions to prove maximal L^q regularity for Cauchy problem: du/dt - Lu(t)=f(t). Mainly we only require "off-diagonal" estimates on the real semigroup (e^tL)_t>0 to obtain maximal L^q regularity. The main idea is to use a one kind of Hardy space H¹ adapted to this problem and then use interpolation results. These techniques permit us to prove weighted maximal regularity too.

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