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Local approximations and intrinsic characterization of spaces of smooth functions on regular subsets of ℝ n
Author(s) -
Shvartsman Pavel
Publication year - 2006
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200510418
Subject(s) - mathematics , characterization (materials science) , sobolev space , approximations of π , pure mathematics , besov space , mathematical analysis , combinatorics , interpolation space , functional analysis , chemistry , physics , biochemistry , gene , optics
We give an intrinsic characterization of the restrictions of Sobolev $W^{k}_{p}$ (ℝ n ), Triebel–Lizorkin $F^{s}_{pq}$ (ℝ n ) and Besov $B^{s}_{pq}$ (ℝ n ) spaces to regular subsets of ℝ n via sharp maximal functions and local approximations. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)