Download Analysis on Gaussian Spaces by Yaozhong Hu PDF

By Yaozhong Hu

Analysis of services at the finite dimensional Euclidean house with admire to the Lebesgue degree is key in arithmetic. The extension to limitless size is a smart problem as a result of the loss of Lebesgue degree on limitless dimensional area. as a substitute the preferred degree utilized in countless dimensional area is the Gaussian degree, which has been unified lower than the terminology of "abstract Wiener space".

Out of the massive quantity of labor in this subject, this publication offers a few primary effects plus contemporary growth. we will current a few effects at the Gaussian area itself corresponding 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 features at the Gaussian house. spinoff, Sobolev areas are brought, whereas the recognized Poincaré inequality, logarithmic inequality, hypercontractive inequality, Meyer's inequality, Littlewood–Paley–Stein–Meyer concept are given in details.

This ebook comprises a few simple fabric that can't be discovered in other places that the writer believes could be a vital part of the topic. for instance, the publication comprises a few fascinating and demanding inequalities, the Littlewood–Paley–Stein–Meyer idea, and the Hörmander theorem. The publication additionally comprises a few fresh growth accomplished by way of the writer and collaborators on density convergence, numerical ideas, neighborhood times.

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