Titlebook: Square Roots of Elliptic Systems in Locally Uniform Domains; Sebastian Bechtel Book 2024 The Editor(s) (if applicable) and The Author(s),

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替代品

Accede

Book 2024end. The centerpiece of the book is the solution to Kato‘s square root problem on locally uniform domains. The Kato result is complemented by corresponding Lᵖ bounds in natural intervals of integrability parameters..This book will be useful to researchers in harmonic analysis, functional analysis and related areas..

MIME

Customary

A Short Account on Sectorial and Bisectorial Operators,in divergence form (sectorial operators), which we will introduce in the subsequent Chap. ., and their associated first-order formulations (bisectorial operators), which we study in more detail in Chap. .. Functional calculus theory will be heavily and freely used in large parts of this book.

疲惫的老马

eulogize

Sobolev Spaces with a Vanishing Trace Condition,gular sets (see Definition 8.1) and include the Ahlfors–David regular sets that we already studied in the last chapter. Eventually, we will also define (fractional) Sobolev spaces on an open set . with and without a vanishing trace condition. To develop the full theory of these spaces, we introduce

murmur

好开玩笑

,Calderón–Zygmund Decomposition for Sobolev Functions,ns, where good means small in a certain sense and the bad functions can be large but are at least localized in a good sense. The classical Calderón–Zygmund decomposition happens at the level of Lebesgue spaces. Here, we show a decomposition in .-spaces.

拉开这车床

Introduction, in these articles are formulated in a more general manner. We tried to reduce technical difficulties as much as possible so that the reader gets an introduction to state-of-the-art results for square roots of elliptic systems in open sets with the least technical overhead possible.