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Analysis on Gaussian Spaces by Yaozhong Hu

By Yaozhong Hu

Analysis of capabilities at the finite dimensional Euclidean house with recognize to the Lebesgue degree is key in arithmetic. The extension to limitless size is a brilliant problem a result of loss of Lebesgue degree on endless dimensional area. in its place the preferred degree utilized in limitless dimensional house is the Gaussian degree, which has been unified lower than the terminology of "abstract Wiener space".

Out of the big quantity of labor in this subject, this booklet offers a few basic effects plus contemporary development. we will current a few effects at the Gaussian area itself resembling the Brunn–Minkowski inequality, Small ball estimates, huge tail estimates. the bulk a part of this booklet is dedicated to the research of nonlinear services 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 across somewhere else that the writer believes might be an essential component of the topic. for instance, the e-book contains a few attention-grabbing and critical inequalities, the Littlewood–Paley–Stein–Meyer thought, and the Hörmander theorem. The ebook additionally contains a few fresh growth accomplished by way of the writer and collaborators on density convergence, numerical strategies, neighborhood times.

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