Weighted boundedness of multilinear maximal function using Dirac deltas
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In this article we extend a method of Miguel de Guzmán involving boundedness properties of maximal functions using Dirac deltas to multilinear setting. This method involves estimating maximal functions over finite linear combination of Dirac deltas. As an application, we obtain end-point weighted boundedness of the multilinear Hardy–Littlewood fractional maximal function with respect to multilinear weights.
KeywordsMaximal function Weighed inequalities Multilinear operators
Mathematics Subject Classification42B25 42B20
We thank the anonymous referee for his/her valuable suggestions that helped to improve the article. Also, the first author expresses his sincere gratitude to his thesis supervisor Prof. Parasar Mohanty for many fruitful discussions. Funding was provided by Ministry of Human Resource Development (Grant No. MHRD Gate-2013). The third author thanks Council of Scientific and Industrial Research for their financial support.
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