Nonlinear Approximation and Muckenhoupt Weights

Autor:	Dominique Picard, Gerard Kerkyacharian
Rok vydání:	2006
Předmět:	Mathematics::Functional Analysis Pure mathematics Basis (linear algebra) Representation theorem General Mathematics Banach space Muckenhoupt weights Hardy space Algebra Computational Mathematics symbols.namesake Lorentz space symbols Interpolation space Lp space Analysis Mathematics
Zdroj:	Constructive Approximation. 24:123-156
ISSN:	1432-0940 0176-4276
DOI:	10.1007/s00365-005-0618-5
Popis:	In the general atomic setting of an unconditional basis in a (quasi-) Banach space, we show that representing the spaces of m-terms approximation as Lorentz spaces is equivalent to the verification of two inequalities (Jackson and Bernstein), and that the validity of these two properties is equivalent to the Temlyakov property. The proof is very direct and, especially, does not use interpolation theory. We apply this result to establish a representation theorem when the norm of the (quasi-) Banach space is given by a quadratic variation formula (thanks to a condition called the p-reverse inequality). This quadratic variation framework is in fact very rich and contains, as examples, the cases of Hardy spaces. We also consider the cases of "weighted" Hardy and Lebesgue spaces when the weight belongs to a Muckenhoupt class and the basis is a wavelet basis. This provides a new example of bases well adapted to approximation.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::cc8117ea89edad299b5523beda93ccd6 https://doi.org/10.1007/s00365-005-0618-5 Zobrazit plný text záznamu Plný text ve formátu PDF