By Yaozhong Hu
Analysis of services at the finite dimensional Euclidean house with admire to the Lebesgue degree is prime in arithmetic. The extension to countless measurement is a smart problem as a result of loss of Lebesgue degree on endless dimensional house. as a substitute the most well-liked degree utilized in endless dimensional area is the Gaussian degree, which has been unified less than the terminology of "abstract Wiener space".
Out of the massive quantity of labor in this subject, this e-book provides a few basic effects plus fresh development. we will current a few effects at the Gaussian house itself similar to the Brunn–Minkowski inequality, Small ball estimates, huge tail estimates. the bulk a part of this publication is dedicated to the research of nonlinear capabilities at the Gaussian area. by-product, Sobolev areas are brought, whereas the recognized Poincaré inequality, logarithmic inequality, hypercontractive inequality, Meyer's inequality, Littlewood–Paley–Stein–Meyer conception are given in details.
This booklet contains a few uncomplicated fabric that can't be came upon in different places that the writer believes will be an essential component of the topic. for instance, the booklet contains a few attention-grabbing and critical inequalities, the Littlewood–Paley–Stein–Meyer concept, and the Hörmander theorem. The ebook additionally contains a few fresh development completed by means of the writer and collaborators on density convergence, numerical suggestions, neighborhood times.
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