On weights satisfying parabolic Muckenhoupt conditions. (January 2016)

• Record Type: Journal Article
• Authors: Kinnunen, Juha; Saari, Olli
• Is Part Of: Nonlinear analysis. Volume 131(2016)
• Page Start: 289
• Page End: 299
• Publication Date: 2016-01
• Subjects: 42B25 -- 42B37 -- 35K55; Weighted norm inequalities -- Bounded mean oscillation -- Doubly nonlinear equation; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2015.07.014
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: This note collects results related to parabolic Muckenhoupt A p weights for a doubly nonlinear parabolic partial differential equation. A general approach is proposed, which extends the theory beyond the quadratic growth case. In particular, the natural parabolic geometry for the equation and the unavoidable time lag are incorporated in the definitions and results. The limiting Muckenhoupt conditions of A ∞ type are also discussed and several open questions are posed.