This book is about differentiation of functions. It is divided into two parts, which can be used
as different textbooks, one for an advanced undergraduate course in functions of one …

Includes material for a standard graduate class, advanced material not covered by the
standard course but necessary in order to read research literature in the area, and extensive …

We define Sobolev space W 1, p for 1< p≤∞ on an arbitrary metric space with finite
diameter and equipped with finite, positive Borel measure. In the Euclidean case it coincides …

The theory of linear Volterra Integro-differental equations has been developing rapidly in the
last three decades. This book provides an easy-to-read, concise introduction to the theory of …

This book provides the reader with the principal concepts and results related to differential
properties of measures on infinite dimensional spaces. In the finite dimensional case such …

A new identity for the entropy of a non-linear image of a measure on is obtained, which
yields the well-known Talagrand's inequality. Triangular mappings on and are studied, that …

rDA ºf also lies in T". The same argument then shows that rDU, is in T: Page 1 76 WS Cohn
order k + 1 is preserved by the operators E and E. Therefore the function rDA ºf also lies in T" …

AD-O. Ukhlov, “On mappings generating the embeddings of Sobolev spaces”, Sibirsk. Mat.
Zh., 34:1 (1993), 185–192; Siberian Math. J., 34:1 (1993), 165–171 Sibirskii …

In this paper, we establish the existence of a stochastic flow of Sobolev diffeomorphisms
R^d∋x\quad⟼\quads,t(x)∈R^d,\qquads,t∈R for a stochastic differential equation (SDE) of …

Homeomorphisms in the Sobolev space W Page 1 J. reine angew. Math. 644 (2010), 221—235
DOI 10.1515/CRELLE.2010.057 Journal für die reine und angewandte Mathematik ( Walter de …