Foundations of Symmetric Spaces of Measurable Functions: Lorentz, Marcinkiewicz and Orlicz Spaces

Description

Key definitions and results in symmetric spaces, particularly Lp, Lorentz, Marcinkiewicz and Orlicz spaces are emphasized in this textbook. A comprehensive overview of the Lorentz, Marcinkiewicz and Orlicz spaces is presented based on concepts and results of symmetric spaces. Scientists and researchers will find the application of linear operators, ergodic theory, harmonic analysis and mathematical physics noteworthy and useful. This book is intended for graduate students and researchers in mathematics and may be used as a general reference for the theory of functions, measure theory, and functional analysis. This self-contained text is presented in four parts totaling seventeen chapters to correspond with a one-semester lecture course. Each of the four parts begins with an overview and is subsequently divided into chapters, each of which concludes with exercises and notes. A chapter called “Complements” is included at the end of the text as supplementary material to assist students with independent work.  Front Matter....Pages i-xvii Front Matter....Pages 1-3 Definition of Symmetric Spaces....Pages 5-15 Spaces L p ,  1 ≤ p ≤ ∞ ....Pages 17-27 The Space L 1 ∩L ∞ ....Pages 29-40 The Space L 1 +L ∞ ....Pages 41-56 Front Matter....Pages 57-58 Embeddings L1 ∩ L∞ ⊆ X ⊆ L1 + L∞ ⊆ L0 ....Pages 59-70 Embeddings. Minimality and Separability. Property (A)....Pages 71-81 Associate Spaces....Pages 83-93 Maximality. Properties (B) and (C)....Pages 95-110 Front Matter....Pages 111-113 Lorentz Spaces....Pages 115-125 Quasiconcave Functions....Pages 127-137 Marcinkiewicz Spaces....Pages 139-150 Embedding \(\varLambda _{\widetilde{V }}^{0}\) ⊆ X ⊆ MV* ....Pages 151-167 Front Matter....Pages 169-170 Definition and Examples of Orlicz Spaces....Pages 171-182 Separable Orlicz Spaces....Pages 183-193 Duality for Orlicz Spaces....Pages 195-205 Comparison of Orlicz Spaces....Pages 207-216 Intersections and Sums of Orlicz Spaces....Pages 217-235 Back Matter....Pages 237-259