函数结构

preface

i decompositions of functions

1 introduction， heuristics， and preliminaries

2 spaces on rn： the regular case

3 spaces on rn： the general case

4 an application： the fubini property

5 spaces on domains： localization and hardy inequalities

6 spaces on domains： decompositions

7 spaces on manifolds

8 taylor expansions of distributions

9 traces on sets， related function spaces and their decompositions

ii sharp inequalities

10 introduction： outline of methods and results

11 classical inequalities

12 envelopes

13 the critical case

14 the super-critical case

15 the sub-critical case

16 hardy inequalities

17 complements

.iii fractal elliptic operators

18 introduction

19 spectral theory for the fractal laplacian

20 the fractal dirichlet problem

21 spectral theory on manifolds

22 isotropic fractals and related function spaces

23 isotropic fractal drums

iv truncations and semi-linear equations

24 introduction

25 truncations

26 the q-operator

27 semi-linear equations； the q-method

references

symbols

index

this book is mainly based on the results of the author and his co-workers ob-tained in the last few years. we tried to present the material in such a way that the main ideas can be understood independently of the existing literature. on the other hand， after proving in chapter i that the function spaces introduced via quarkonial decompositions coincide with the well-established spaces b8pq and fspq we feel free to use known results about these spaces， especially when we have nothing new to say about the assertions used. a reader who is mostly interested in the material presented in one of the chapters ii， iii， or iv， which are largely independent of each other， may skip chapter i， at the first glance.but most of the related proofs in these chapters depend substantially on the theory developed in the first chapter.
it is a pleasure to acknowledge the great help i have received from my col-laborators in jena， in particular dorothee haroske and winfried sickel， who made valuable suggestions which have been incorporated in the text. i am especially indebted to dorothee haroske for producing all the figures in this book. last， but not least， i wish to thank my friend and colleague david edmunds in brighton who looked through the whole manuscript and offered many comments.