Gaussian Harmonic Analysis

• Chapter 1- Preliminary Results.- Chapter 2- The Ornstein-Uhlenbeck Operator and the Ornstein-Uhlenbeck Semigroup.- Chapter 3- The Poisson-Hermite Semigroup.- Chapter 4- Covering Lemmas, Gaussian Maximal Functions, and Calderón-Zygmund Operators.- Chapter 5- Littlewood-Paley-Stein Theory with respect to γd.- Chapter 6- Spectral Multiplier Operators with respect to γd.- Chapter 7- Function Spaces with respect to γd.- Chapter 8- Gaussian Fractional Integrals and Fractional Derivatives.- Chapter 9- Singular Integrals with respect to γd.- Appendix.- References.- Index.

“This book is the first comprehensive account of Gaussian harmonic analysis, and as such is a most welcome addition to the literature suitable for experts in the field and advanced graduate students who want to learn the subject.” (Jan van Neerven, Mathematical Reviews, September, 2020)“This well-written and organized (mainly self-contained) book is a reader-friendly manual in the field of Gaussian harmonic analysis. It can be recommended for experts and for graduate, postgraduate and doctoral students.” (Michael Perelmuter, zbMATH 1421.42001, 2019)