## Approximation of Functions in the Mean |

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### Contents

Besov O V The behavior of differentiable functions at infinity and | 3 |

Besov O V and Dzabrailov A D Interpolation theorems for some spaces | 15 |

Besov O V Classes of functions with a generalized mixed Holder condi | 21 |

I On the additivity of the spaces W and B and on imbed | 30 |

Volkov E A On differential properties of solutions of the Laplace | 54 |

Kazarjan G G Estimates of mixed derivatives in L by differential poly | 66 |

Lizorkin P I Generalized Liouville differentiation and the method of multi | 105 |

Lizorkin P I and Nikolskii S M The compactness of sets of differenti | 168 |

Nikolskii Ju S On imbedding theorems of weight classes HwKOJlbCKHH | 178 |

Nikol skii Ju S Singular integral operators with weight spaces | 190 |

Pigolkina T S On the theory of weight classes IlnrOJlKHHa T C | 201 |

Timan T A Existence conditions and estimates of transforms of the Cal | 213 |

230 | |

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### Common terms and phrases

addition Akad Amer applying arbitrary boundary values bounded boundedness change of variables class of functions coefficients coincides compact support conditions of Theorem consider constant independent convolution coordinates corresponding defined definition denote Dirichlet Dirichlet problem Dokl English transl equation equivalent exists finite fixed formula Fourier images Fourier transform func function f function spaces functions with compact Hence Holder condition Holder inequality hyperplane imbedding theorems infinitely differentiable function integer J. E. Littlewood kernel G Laplace equation Lemma Let the function Minkowski inequality mixed derivatives Nauk SSSR norm notation O. V. Besov one-dimensional oo oo operator P. I. Lizorkin parallelepiped polynomials positive integer Proc proof of Theorem properties proved representation right-hand side satisfies the condition seminorm similar Singular integral operators smooth function Sobolev spaces solution Soviet Math Steklov Inst theory tion Trudy Mat vector weight classes zero