Theory of Henstock–Orlicz Spaces
Buch in deiner Nähe kaufen
Beschreibung
This book presents a systematic treatment of Henstock–Orlicz (or H-Orlicz) spaces with minimal assumptions on the Young function. H-Orlicz spaces contain non-absolute integrable functions called Henstock–Kurzweil integrable functions. Results from classical functional analysis are presented in detail, and new material is included on classical analysis. Extrapolation is used to prove, for example, the countable additivity of Henstock–Dunford integrable functions on H-Orlicz spaces are included. Relationships of modular convergence and norm convergence of H-Orlicz spaces are discussed. Finally, central geometrical results are provided for H-spaces, including uniformly convexity, reflexivity and the Radon–Nikodym property of the Henstock–Orlicz spaces. Primarily aimed at researchers and PhD students interested in Orlicz spaces or generalized Orlicz spaces, this book can be used as a basis for advanced graduate courses in analysis.
This book presents a systematic treatment of Henstock–Orlicz (or H-Orlicz) spaces with minimal assumptions on the Young function. H-Orlicz spaces contain non-absolute integrable functions called Henstock–Kurzweil integrable functions. Results from classical functional analysis are presented in detail, and new material is included on classical analysis. Extrapolation is used to prove, for example, the countable additivity of Henstock–Dunford integrable functions on H-Orlicz spaces are included. Relationships of modular convergence and norm convergence of H-Orlicz spaces are discussed. Finally, central geometrical results are provided for H-spaces, including uniformly convexity, reflexivity and the Radon–Nikodym property of the H–Orlicz spaces. Primarily aimed at researchers and PhD students interested in Orlicz spaces or generalized Orlicz spaces, this book can be used as a basis for advanced graduate courses in analysis.
Discusses the Orlicz spaces in vector measure for non-absolute integrable functions Includes non-doubling versions of results for the case of non-absolute integrable functions on Orlicz spaces Presents geometric properties of the Orlicz spaces
Autor*in
Bipan Hazarika
Themen in »Theory of Henstock–Orlicz Spaces«
Banach function space uniformly convex Radon-Nikodym property non-absolute integrals Henstock-Kurzweil integral Young functions Orlicz spaces modular convergence norm convergence Henstock-Dunford functions Henstock-Pettis integrable functions Henstock-Orlicz space Countable additivity vector measure Banach valued functions