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