Weighted square function inequalities
Osekowski, Adam (University of Warsaw (Polònia). Department of Mathematics, Informatics and Mechanics)

Date:	2018
Abstract:	For an integrable function f on [0, 1)d, let S(f) and M f denote the corresponding dyadic square function and the dyadic maximal function of f, respectively. The paper contains the proofs of the following statements. (i) If w is a dyadic A1 weight on [0, 1)d, then $l 1(w). The exponent 1/2 is shown to be the best possible. (ii) For any p > 1, there are no constants cp, αp epending only on p such that for all dyadic Ap weights w on [0, 1)d, $l 1(w). $l 1(w) ≤√ 5[w] 1/2 A1 $l 1(w) ≤ cp[w] αp Ap $m f $s (f).
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Square function ; Maximal operator ; Dyadic, weight ; Bellman function
Published in:	Publicacions matemàtiques, Vol. 62 Núm. 1 (2018) , p. 75-94 (Articles) , ISSN 2014-4350

Adreça alternativa: https://raco.cat/index.php/PublicacionsMatematiques/article/view/329928
DOI: 10.5565/PUBLMAT6211804

20 p, 392.3 KB

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