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