Hardy operators, function spaces and embeddings
著者
書誌事項
Hardy operators, function spaces and embeddings
（Springer monographs in mathematics）
Springer, c2004
- : pbk
大学図書館所蔵 全1件
注記
"Softcover reprint of the hardcover 1st edition 2004"--T.p. verso
Includes bibliographical references (p. [307]-317) and index
"With 6 figures"--T.p.
内容説明・目次
内容説明
Classical Sobolev spaces, based on Lebesgue spaces on an underlying domain with smooth boundary, are not only of considerable intrinsic interest but have for many years proved to be indispensible in the study of partial differential equations and variational problems. Many developments of the basic theory since its inception arise in response to concrete problems, for example, with the (ubiquitous) sets with fractal boundaries.
The theory will probably enjoy substantial further growth, but even now a connected account of the mature parts of it makes a useful addition to the literature. Accordingly, the main themes of this book are Banach spaces and spaces of Sobolev type based on them; integral operators of Hardy type on intervals and on trees; and the distribution of the approximation numbers (singular numbers in the Hilbert space case) of embeddings of Sobolev spaces based on generalised ridged domains.
This timely book will be of interest to all those concerned with the partial differential equations and their ramifications. A prerequisite for reading it is a good graduate course in real analysis.
目次
1 Preliminaries.- 2 Hardy-type Operators.- 3 Banach function spaces.- 4 Poincare and Hardy inequalities.- 5 Generalised ridged domains.- 6 Approximation numbers of Sobolev embeddings.- References.- Author Index.- Notation Index.
「Nielsen BookData」 より