Mathematics and Statistics Vol. 1(3), pp. 144 - 156
DOI: 10.13189/ms.2013.010306
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Criteria of Two-weighted Inequalities for Multidimensional Hardy Type Operator in Weighted Musielak-Orlicz Spaces and Some Application

Rovshan A. Bandaliev^1,2,*
1 Institute of Mathematics and Mechanics, Baku, Azerbaijan
² Baku, Azerbaijan, Az 1141, B. Vahabzade str., 9

ABSTRACT

In this paper a two-weight criterion for multidimensional Hardy type operator and its dual operator acting from weighted Lebesgue spaces into weighted Musielak-Orlicz spaces is proved. As application we prove the boundedness of multidimensional geometric mean operator in the weighted Musielak-Orlicz spaces. In particular, from obtained results implies the boundedness of multidimensional Hardy operator and its dual operator acting from usual weighted Lebesgue spaces into weighted variable Lebesgue spaces. In this paper we establish integral-type necessary and sufficient condition on weights, which provides the boundedness of the multidimensional Hardy type operator from weighted Lebesgue spaces into weighted Musielak-Orlicz spaces.

KEYWORDS
Weights, Weighted Musielak-Orlicz Space, Hardy Type Operator, Multidimensional Geometric Mean Operator, Boundedness

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Rovshan A. Bandaliev , "Criteria of Two-weighted Inequalities for Multidimensional Hardy Type Operator in Weighted Musielak-Orlicz Spaces and Some Application," Mathematics and Statistics, Vol. 1, No. 3, pp. 144 - 156, 2013. DOI: 10.13189/ms.2013.010306.

(b). APA Format:
Rovshan A. Bandaliev (2013). Criteria of Two-weighted Inequalities for Multidimensional Hardy Type Operator in Weighted Musielak-Orlicz Spaces and Some Application. Mathematics and Statistics, 1(3), 144 - 156. DOI: 10.13189/ms.2013.010306.