By Yaozhong Hu
Analysis of services at the finite dimensional Euclidean house with appreciate to the Lebesgue degree is key in arithmetic. The extension to limitless measurement is a smart problem as a result loss of Lebesgue degree on countless dimensional house. as an alternative the preferred degree utilized in countless dimensional area is the Gaussian degree, which has been unified below the terminology of "abstract Wiener space".
Out of the massive volume of labor in this subject, this booklet provides a few primary effects plus contemporary development. we will current a few effects at the Gaussian area itself akin to the Brunn–Minkowski inequality, Small ball estimates, huge tail estimates. the bulk a part of this ebook is dedicated to the research of nonlinear features at the Gaussian area. 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 booklet comprises a few easy fabric that can not be stumbled on in other places that the writer believes can be an essential component of the topic. for instance, the ebook contains a few attention-grabbing and demanding inequalities, the Littlewood–Paley–Stein–Meyer thought, and the Hörmander theorem. The booklet additionally contains a few contemporary development accomplished by way of the writer and collaborators on density convergence, numerical suggestions, neighborhood times.
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