## Constants in some inequalities of analysisPresents the results of the author's research on some of the inequalities that arise in calculus and functional analysis, such as estimates for the norm of an operator, error estimates in numerical methods, estimates for the norm of a function that is extended to some larger domain, and inequalities characterizing the accuracy in approximating a function. Mikhlin gives solutions to one or both of the problems associated with the constants that appear in some of these inequalities: determining the best constant that assures that the inequality will hold, or evaluating some numerical value of the constant for which the inequality is considered true. |

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### Contents

Preface | 7 |

The smallest extension constant for PFlfunctions | 22 |

Some inequalities in the theory of Sobolev spaces | 45 |

Copyright | |

3 other sections not shown

### Common terms and phrases

A. A. Markov assume ball basic functions book 11 boundary conditions bounded domain Chap coefficient cone condition consider constant C0 coordinate cube Q defined derivatives Dirichlet problem domain Q eigenvalue equal equation Euclidean space extended function extension of functions extension procedure finite element approximation following estimate func function u(x functions belonging Furthermore Heine-Borel Theorem hence Hestenes holds integer Laplace operator Let Q Lipschitz-continuous Lp(Em Lr(Em means minimal norm Minkowski's inequality multi-index multiplicative mollifier Neumann problem notations obtain one-dimensional optimal polynomials partition of unity piecewise polynomials positive integer present section preserving the class problem replace resp right-hand side smallest extension constant Sobolev spaces star-like Stirling's formula summand theorem tion uh(x vanish vector virtue want to estimate whole space Wp(Em Wp{Q WsP{Q Young's inequality