By Yaozhong Hu
Analysis of capabilities at the finite dimensional Euclidean area with recognize to the Lebesgue degree is key in arithmetic. The extension to limitless size is a brilliant problem because of the loss of Lebesgue degree on endless dimensional area. as an alternative the preferred 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 volume 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 area itself akin 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 house. spinoff, 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 e-book contains a few easy fabric that can not be chanced on in other places that the writer believes may be an essential component of the topic. for instance, the booklet comprises a few fascinating and significant inequalities, the Littlewood–Paley–Stein–Meyer concept, and the Hörmander theorem. The booklet additionally comprises a few contemporary growth completed by way of the writer and collaborators on density convergence, numerical strategies, neighborhood times.
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Analysis on Gaussian Spaces by Yaozhong Hu