On Necessary And Sufficient Conditions For L P Estimates Of Riesz Transforms Associated To Elliptic Operators On Mathbb R N And Related Estimates
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On Necessary and Sufficient Conditions for $L^p$-Estimates of Riesz Transforms Associated to Elliptic Operators on $\mathbb {R}^n$ and Related Estimates
Author: Pascal Auscher
language: en
Publisher: American Mathematical Soc.
Release Date: 2007
This memoir focuses on $Lp$ estimates for objects associated to elliptic operators in divergence form: its semigroup, the gradient of the semigroup, functional calculus, square functions and Riesz transforms. The author introduces four critical numbers associated to the semigroup and its gradient that completely rule the ranges of exponents for the $Lp$ estimates. It appears that the case $p2$ which is new. The author thus recovers in a unified and coherent way many $Lp$ estimates and gives further applications. The key tools from harmonic analysis are two criteria for $Lp$ boundedness, one for $p2$ but in ranges different from the usual intervals $(1,2)$ and $(2,\infty)$.
History of Banach Spaces and Linear Operators
Author: Albrecht Pietsch
language: en
Publisher: Springer Science & Business Media
Release Date: 2007-12-31
Written by a distinguished specialist in functional analysis, this book presents a comprehensive treatment of the history of Banach spaces and (abstract bounded) linear operators. Banach space theory is presented as a part of a broad mathematics context, using tools from such areas as set theory, topology, algebra, combinatorics, probability theory, logic, etc. Equal emphasis is given to both spaces and operators. The book may serve as a reference for researchers and as an introduction for graduate students who want to learn Banach space theory with some historical flavor.
Black Holes in Higher Dimensions
Author: Gary T. Horowitz
language: en
Publisher: Cambridge University Press
Release Date: 2012-04-19
The first book devoted to black holes in more than four dimensions, for graduate students and researchers.