《索伯列夫空间和插值空间导论》是以作者研究生教程的讲义为蓝本整理扩充而成，全面讲述了索伯列夫空间和插值理论。书中包括42章，每章尽可能多的包括研究生学习所需的材料，不仅是一部研究生学习的讲义材料，也是很多老师学者关心的课题。通过大量的脚注讲述了本教程的形成过程有关老师的趣闻轶事，这使本书不仅是一本很完善的教程，而且也非常适用于相关专业的科研人员。
目次：历史背景；勒贝格测度，卷积；卷积光滑；阶段，radon测度和分布；张量积密度，结果；支集观点扩充；索伯列夫嵌入理论：1[=p[n；索伯列夫嵌入定理，n[=p[无穷；庞加莱不等式；平衡定理：紧嵌入；边界的一般性，结果；边界上的迹；格林公式；傅里叶变换；hs（rn）迹；太小点的证明；紧嵌入；lax-milgram定理；h（div，ω）空间；插值的背景，复杂方法；实插值，k方法；具有权重的l2空间的插值；实插值，j方法；插值不等式，lions-peetre反复定理；最大函数；双线性和非线性插值；通过插值获得lp，运用规范；索伯列夫嵌入定理方法；索伯列夫嵌入定理综述；定义索伯列夫空间和besov空间； 性质； 的性质；bv空间中变量；用插值空间代替bv空间；伪线性双曲系统的激波；插值空间成为迹空间；插值空间中的对偶和紧性；混合问题；参考信息；缩写和数学符号。
读者对象：数学专业的研究生和科研人员。
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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