By Yaozhong Hu
Analysis of features at the finite dimensional Euclidean house with recognize to the Lebesgue degree is prime in arithmetic. The extension to endless measurement is a brilliant problem as a result of the loss of Lebesgue degree on limitless dimensional area. in its place the most well-liked degree utilized in endless dimensional area is the Gaussian degree, which has been unified lower than the terminology of "abstract Wiener space".
Out of the massive volume of labor in this subject, this publication offers a few primary effects plus fresh growth. we will current a few effects at the Gaussian area itself comparable to the Brunn–Minkowski inequality, Small ball estimates, huge tail estimates. the bulk a part of this booklet is dedicated to the research of nonlinear features 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 ebook comprises a few simple fabric that can not be stumbled on in other places that the writer believes might 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 publication additionally contains a few contemporary growth accomplished through the writer and collaborators on density convergence, numerical recommendations, neighborhood times.
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Analysis on Gaussian Spaces by Yaozhong Hu