《索伯列夫空間和插值空間導論》是以作者研究生教程的講義為藍本整理擴充而成，全面講述了索伯列夫空間和插值理論。書中包括42章，每章盡可能多的包括研究生學習所需的材料，不僅是一部研究生學習的講義材料，也是很多老師學者關心的課題。通過大量的腳注講述了本教程的形成過程有關老師的趣聞軼事，這使本書不僅是一本很完善的教程，而且也非常適用于相關專業(yè)的科研人員。
目次：歷史背景；勒貝格測度，卷積；卷積光滑；階段，radon測度和分布；張量積密度，結(jié)果；支集觀點擴充；索伯列夫嵌入理論：1[=p[n；索伯列夫嵌入定理，n[=p[無窮；龐加萊不等式；平衡定理：緊嵌入；邊界的一般性，結(jié)果；邊界上的跡；格林公式；傅里葉變換；hs（rn）跡；太小點的證明；緊嵌入；lax-milgram定理；h（div，ω）空間；插值的背景，復雜方法；實插值，k方法；具有權(quán)重的l2空間的插值；實插值，j方法；插值不等式，lions-peetre反復定理；最大函數(shù)；雙線性和非線性插值；通過插值獲得lp，運用規(guī)范；索伯列夫嵌入定理方法；索伯列夫嵌入定理綜述；定義索伯列夫空間和besov空間； 性質(zhì)； 的性質(zhì)；bv空間中變量；用插值空間代替bv空間；偽線性雙曲系統(tǒng)的激波；插值空間成為跡空間；插值空間中的對偶和緊性；混合問題；參考信息；縮寫和數(shù)學符號。
讀者對象：數(shù)學專業(yè)的研究生和科研人員。
1 historical background
2 the lebesgue measure, convolution
3 smoothing by convolution
4 truncation; radon measures; distributions
5 sobolev spaces; multiplication by smooth functions
6 density of tensor products; consequences
7 extending the notion of support
8 sobolev's embedding theorem, i ≤ p ＜ n
9 sobolev's embedding theorem, n ≤ p≤∞
10 poincare's inequality
11 the equivalence lemma; compact embeddings
12 regularity of the boundary; consequences
13 traces on the boundary
14 (green's formula
15 the fourier transform
1 historical background
2 the lebesgue measure, convolution
3 smoothing by convolution
4 truncation; radon measures; distributions
5 sobolev spaces; multiplication by smooth functions
6 density of tensor products; consequences
7 extending the notion of support
8 sobolev's embedding theorem, i ≤ p ＜ n
9 sobolev's embedding theorem, n ≤ p≤∞
10 poincare's inequality
11 the equivalence lemma; compact embeddings
12 regularity of the boundary; consequences
13 traces on the boundary
14 (green's formula
15 the fourier transform
16 traces of hs(rn)
17 proving that a point is too small
18 compact embeddings
19 lax-milgram lemma
.20 the space h(div;ω)
21 background on interpolation; the complex method
22 real interpolation; k-method
23 interpolation of l2 spaces with weights
24 real interpolation; j-method
25 interpolation inequalities, the spaces (e0, e1)θ,1
26 the lions-peetre reiteration theorem
27 maximal functions
28 bilinear and nonlinear interpolation
29 obtaining lp by interpolation, with the exact norm
30 my approach to sobolev's embedding theorem
31 my generalization of sobolev's embedding theorem
32 sobolev's embedding theorem for besov spaces
33 the lions-magenes space h1/2∞(ω)
34 defining sobolev spaces and besov spaces for ω
35 characterization of ws,p(rn)
36 characterization of ws,p(ω)
37 variants with bv spaces
38 replacing bv by interpolation spaces
39 shocks for quasi-linear hyperbolic systems
40 interpolation spaces as trace spaces
41 duality and compactness for interpolation spaces
42 miscellaneous questions
43 biographical information
44 abbreviations and mathematical notation
references
index
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