Maximal Functions, Littlewood-Paley Theory, Riesz Transforms and Atomic Decomposition in the Multi-Parameter Flag Setting.

Cover
Title page
Acknowledgement
Notation
Chapter 1. Introduction and Statement of Main Results, Applications
1.1. Background and Main Results
1.2. Statement of Main Results
1.3. Strategy of Proofs of the Main Results
1.4. Applications and Related Open Questions
Chapter 2. Flag Littlewood-Paley Estimate: | _{ }( )|₁, | _{ }( )|₁ and | _{ }( )|₁
2.1. Discrete Calderón Reproducing Formula
2.2. Flag Plancherel-Pólya Type Inequalities
2.3. The Equivalence of | _{ }( )|₁ and | _{ }( )|₁
2.4. The Estimate | _{ }( )|₁ ₂₂₇₂ | _{ }( )|₁
Chapter 3. Estimates of Area Functions, Maximal Functions and Riesz Transforms via Flag Poisson Integral Technique
3.1. The Estimate | _{ }( )|₁ ₂₂₇₂ | *|₁
3.2. The Estimate | *|₁ ₂₂₇₂ | ⁺|₁
3.3. The Estimate | ⁺|₁ ₂₂₇₂ ₂₂₁₁ ₂ ₇ ₂₀₈ ₁^{ + }∑_{ =1}^{ }| _{ , }( )|₁+| |₁
Chapter 4. Flag Maximal Functions: from Poisson Kernel to General Schwartz Kernels
4.1. The Equivalence | *|₁ ₂₂₄₈ | *ᵩ( )|₁
4.2. The Equivalence | ⁺|₁ ₂₂₄₈ | ⁺ ¹ ⁶⁹ ( )|₁
Chapter 5. Atomic Decompositions of Flag Hardy Spaces
5.1. Heat Kernel and Finite Speed Propagation
5.2. Atomic Decomposition for ¹_{ }(ℝⁿ×ℝ^{ }).
5.3. Proof of the Atomic Decomposition
Chapter 6. Estimates of Riesz Transforms and Area Function via Atomic Decomposition
Bibliography
Back Cover.