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Table of Contents
Cover
Title page
Introduction
Chapter 1. Quantum Euclidean spaces
1.1. Crossed product form
1.2. Metrics and derivations
1.3. Quantum Euclidean variables
Chapter 2. Calderón-Zygmund _{ } theory
2.1. Kernels and symbols
2.2. CZ extrapolation: Model case
2.3. CZ extrapolation: General case
Chapter 3. Pseudodifferential _{ } calculus
3.1. Adjoint and product formulae
3.2. ₂-boundedness: Sufficient conditions
3.3. _{ }-boundedness and Sobolev -estimates
Chapter 4. _{ } regularity for elliptic PDEs
Appendix A. Noncommutative tori
Appendix B. BMO space theory in \RR_{Θ}
B.1. Operator space structures on \BMO and \Hardy₁
B.2. The \Hardy₁-\BMO duality
B.3. Complex interpolation
B.4. An auxiliary density result
Bibliography
Back Cover.
Title page
Introduction
Chapter 1. Quantum Euclidean spaces
1.1. Crossed product form
1.2. Metrics and derivations
1.3. Quantum Euclidean variables
Chapter 2. Calderón-Zygmund _{ } theory
2.1. Kernels and symbols
2.2. CZ extrapolation: Model case
2.3. CZ extrapolation: General case
Chapter 3. Pseudodifferential _{ } calculus
3.1. Adjoint and product formulae
3.2. ₂-boundedness: Sufficient conditions
3.3. _{ }-boundedness and Sobolev -estimates
Chapter 4. _{ } regularity for elliptic PDEs
Appendix A. Noncommutative tori
Appendix B. BMO space theory in \RR_{Θ}
B.1. Operator space structures on \BMO and \Hardy₁
B.2. The \Hardy₁-\BMO duality
B.3. Complex interpolation
B.4. An auxiliary density result
Bibliography
Back Cover.