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A. Böttcher; M. Seybold : Wackelsatz and Stechkins inequality for discrete Muckenhoupt weights

A. Böttcher; M. Seybold : Wackelsatz and Stechkins inequality for discrete Muckenhoupt weights

Author(s) :
A. Böttcher; M. Seybold
Title :
Wackelsatz and Stechkins inequality for discrete Muckenhoupt weights
Preprint series
Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 99-7, 1999
Mathematics Subject Classification :
42A50 [ Singular integrals, one variable ]
42A45 [ Multipliers, one variable ]
Abstract :
The purpose of this paper is to present full proofs for the important results on discrete Muckenhoupt weights. The first states that if w is a weight in the Muckenhoupt class A_p for l^p, then w^r belongs to A_p for all r sufficiently close to 1 ("Wackelsatz"). The second result is Stechkin's inequality, which gives an upper estimate for the multiplier norm on l^p(w)(w in A_p) through the L^infty norm and the total variation of the multiplier. Although both results are certainly well-known to specialists, we have not found self-contained proofs. to
Keywords :
Muckenhoupt condition, multiplier, Stechkins inequality
Language :
english
Publication time :
8/1999