Theory of function spaces

Hans Triebel0817626395, 9783764326395, 9783034604185, 9780817626396, 3034604181, 3764326395

“Theory of Function Spaces II” deals with the theory of function spaces of type Bspq and Fspq as it stands at the present. These two scales os spaces cover many well-known function spaces such as H?lder-Zygmund spaces, (fractional) Sobolev spaces, Besov spaces, inhomogeneous Hardy spaces, spaces of BMO-type and local approximation spaces which are closely connected with Morrey-Campanato spaces. “Theory of Function Spaces II” is self-contained, although it may be considered an update of the author’s earlier book of the same title. The book’s seven chapters start with a historical survey of the subject, and then analyze the theory of function spaces in Rn and in domains, applications to (exotic) pseudo-differential operators, and function spaces on Riemannian manifolds.

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Table of contents :
Cover……Page 1
Series……Page 2
Title page……Page 3
Date-line……Page 4
Preface……Page 5
Contents……Page 7
1.1 Introduction……Page 9
1.2 Derivatives and differences of functions……Page 10
1.3 The spectral approach……Page 17
1.4 Hardy spaces……Page 28
1.5 The Fourier-analytical approach……Page 35
1.6 Interpolation methods……Page 44
1.7 Local approximation spaces……Page 54
1.8 Local means, traces of harmonic and thermic functions……Page 60
1.9 A new device: Atoms as building blocks……Page 67
1.10 Spaces on domains……Page 76
1.11 Spaces on Riemannian manifolds and Lie groups……Page 83
1.12 Epilogue……Page 93
2.2 Prerequisites……Page 95
2.3 Definitions and basic properties……Page 100
2.4 General characterizations for $F^s_{p,q}$……Page 108
2.5 General characterizations for $B^s_{p,q}$……Page 139
2.6 Concrete characterizations……Page 147
3.1 Introduction……Page 167
3.2 Atomic decompositions of $F^s_{p,q}$……Page 168
3.3 Distinguished representations……Page 181
3.4 Oscillations……Page 187
3.5 Characterizations via oscillations and differences……Page 194
4.1 Introduction……Page 207
4.2 Pointwise multipliers……Page 209
4.3 Diffeomorphisms……Page 214
4.4 Traces……Page 220
4.5 Spaces on $R^n_+$, extensions……Page 229
5.1 Preliminaries……Page 245
5.2 Intrinsic characterizations……Page 248
5.3 Morrey-Campanato spaces, the spaces $C^s_p$……Page 254
5.4 Further problems……Page 260
6.1 Introduction……Page 263
6.2 An approach via local means……Page 264
6.3 An approach via atoms……Page 269
7.2 The spaces $F^s_{p,q}$ on manifolds……Page 289
7.3 The spaces $B^s_{p,q}$ on manifolds……Page 316
7.4 Further properties of the spaces $F^s_{p,q}$ and $B^s_{p,q}$ on manifolds……Page 321
7.5 Characterizations of spaces on manifolds via differences and derivatives……Page 333
7.6 Spaces on Lie groups……Page 345
References……Page 355
Symbols……Page 375
Index……Page 377
Series……Page 379