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Theory of Henstock–Orlicz Spaces / by Bipan Hazarika, Hemanta Kalita.
Springer Nature - Springer Mathematics and Statistics (R0) eBooks 2025 English International Available online
View online- Format:
- Book
- Author/Creator:
- Hazarika, Bipan.
- Series:
- Mathematical Marvels: Texts and Monographs in the Spirit of CR Rao, 3005-1975
- Language:
- English
- Subjects (All):
- Sequences (Mathematics).
- Functions of complex variables.
- Functional analysis.
- Sequences, Series, Summability.
- Several Complex Variables and Analytic Spaces.
- Functional Analysis.
- Local Subjects:
- Sequences, Series, Summability.
- Several Complex Variables and Analytic Spaces.
- Functional Analysis.
- Physical Description:
- 1 online resource (280 pages)
- Edition:
- 1st ed. 2025.
- Place of Publication:
- Singapore : Springer Nature Singapore : Imprint: Springer, 2025.
- Summary:
- 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.
- Contents:
- Chapter 1. Basic Ingredients
- Chapter 2. Orlicz spaces
- Chapter 3. Historical Background of Non-absolute Integrals
- Chapter 4. Kluvánek-Lewis-Henstock Integrals
- Chapter 5. Henstock-Dunford and Henstock-Pettis Integrable Functions
- Chapter 6. Henstock-Orlicz Spaces and Denseness of C
- Chapter 7. Geometrical Properties of Henstock-Orlicz Spaces
- Chapter 8. Weak Henstock-Orlicz Spaces and Inclusion Properties
- Chapter 9. Countable Additivity of Henstock-Dunford Integrable Function and Orlicz Spaces
- Chapter 10 Modular convergence in H-Orlicz spaces of Banach valued functions.
- Notes:
- Description based on publisher supplied metadata and other sources.
- ISBN:
- 981-9695-48-1
- OCLC:
- 1534791582
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