Download e-book for iPad: Analysis on Gaussian Spaces by Yaozhong Hu

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 countless size is a brilliant problem a result of loss of Lebesgue degree on limitless dimensional house. in its place the most well-liked degree utilized in countless dimensional area is the Gaussian degree, which has been unified lower than the terminology of "abstract Wiener space".

Out of the massive quantity of labor in this subject, this ebook provides a few primary effects plus fresh development. we will current a few effects at the Gaussian area 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 services 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 concept are given in details.

This ebook contains a few uncomplicated fabric that can not be came upon in different places that the writer believes will be a vital part of the topic. for instance, the ebook contains a few fascinating and significant inequalities, the Littlewood–Paley–Stein–Meyer concept, and the Hörmander theorem. The booklet additionally contains a few fresh growth completed by means of the writer and collaborators on density convergence, numerical ideas, neighborhood times.

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Analysis on Gaussian Spaces by Yaozhong Hu

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