By Yaozhong Hu
Analysis of features at the finite dimensional Euclidean area with admire to the Lebesgue degree is prime in arithmetic. The extension to limitless size is a smart 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 below the terminology of "abstract Wiener space".
Out of the massive quantity of labor in this subject, this publication provides a few basic effects plus fresh development. we will current a few effects at the Gaussian house itself reminiscent of the Brunn–Minkowski inequality, Small ball estimates, huge tail estimates. the bulk a part of this e-book is dedicated to the research of nonlinear features at the Gaussian house. by-product, Sobolev areas are brought, whereas the recognized Poincaré inequality, logarithmic inequality, hypercontractive inequality, Meyer's inequality, Littlewood–Paley–Stein–Meyer conception are given in details.
This booklet comprises a few simple fabric that can not be came upon in other places that the writer believes may be an essential component of the topic. for instance, the booklet contains a few fascinating and significant inequalities, the Littlewood–Paley–Stein–Meyer conception, and the Hörmander theorem. The publication additionally comprises a few contemporary growth accomplished through the writer and collaborators on density convergence, numerical suggestions, neighborhood times.
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