| Preface 1 Preliminaries 1.1 Notation Inner product of vectors Support of a function Boundary of a set Distance from a point to a set Characteristic function of a set Multi-indices Partial derivative operators Function spaces--continuous， HSlder continuous， HSlder continuous derivatives 1.2 Measures on Rn Lebesgue measurable sets Lebesgue measurability of Borel sets Suslin sets 1.3 Covering Theorems Hausdorff maximal principle General covering theorem Vitali covering theorem Covering lemma, with n-balls whose radii vary in Lips hitzian way Besicovitch covering lemma Besicovitch differentiation theorem 1.4 Hausdorff Measure Equivalen e of Hausdorff and Lebesgue measures Hausdorff dimension 1.5 LP-Spaces Integration of a function via its distribution function Young's inequality Holder's and Jensen's inequality 1.6 Regularization LP-spaces and regularization 1.7 Distributions Functions and measures, as distributions Positive distributions Distributions determined by their lo al behavior Convolution of distributions Differentiation of distributions 1.8 Lorentz Spaces Non-in reasing rearrangement of a fun tion Elementary properties of rearranged functions Lorentz spaces O'Neil's inequality, for rearranged functions Equivalence of LP-norm and (p,p)-norm Hardy's inequality Inclusion relations of Lorentz spaces Exercises Historical Notes Sobolev Spaces and Their Basic Properties 2.1 Weak Derivatives Sobolev spaces Absolute continuity on lines LP-norm of difference quotients Truncation of Sobolev functions Composition of Sobolev functions 2.2 Change of Variables for Sobolev functions Radema her's theorem Bi-Lipschitzian change of variables 2.3 Approximation of Sobolev functions by Smooth functions Partition of unity Smooth functions are dense in Wk'p 2.4 Sobolev Inequalities Sobolev's inequality 2.5 The Relli h-Kondrachov compactness Theorem Extension domains 2.6 Bessel Potentials and apacity Riesz and Bessel kernels Bessel potentials Bessel apacity Basic properties of Bessel apacity Capa itability of Suslin sets Minimax theorem and alternate formulation of Bessel apacity …… 3 Pointwise Behavior of Sobolev Functions 4 Poincare Inequalities 5 Functions of Bounded Variation Bibliography List of Symbols Index |
内容加载中，请稍后...
商品评论（0条）