By Yaozhong Hu
Analysis of services at the finite dimensional Euclidean area with recognize to the Lebesgue degree is key in arithmetic. The extension to endless measurement is a brilliant problem as a result of loss of Lebesgue degree on endless dimensional house. as an alternative the most well-liked degree utilized in countless dimensional house is the Gaussian degree, which has been unified less than the terminology of "abstract Wiener space".
Out of the big volume of labor in this subject, this ebook offers a few basic effects plus fresh growth. 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 services 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 conception are given in details.
This ebook comprises a few simple fabric that can not be came upon in different places that the writer believes could be an essential component of the topic. for instance, the publication contains a few fascinating and significant inequalities, the Littlewood–Paley–Stein–Meyer concept, and the Hörmander theorem. The e-book additionally comprises a few fresh development accomplished by way of the writer and collaborators on density convergence, numerical recommendations, neighborhood times.
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Analysis on Gaussian Spaces by Yaozhong Hu