Some new multidimensional hardy-type inequalities with kernels via convexity | Zendy

James Oguntuase | Zendy; Philip Durojaye | Zendy

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Some new multidimensional hardy-type inequalities with kernels via convexity

Author(s) -

James Oguntuase,

Philip Durojaye

Publication year - 2013

Publication title -

publications de l institut mathematique

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.246

H-Index - 17

eISSN - 1820-7405

pISSN - 0350-1302

DOI - 10.2298/pim1307153o

Subject(s) - convexity , mathematics , hardy space , type (biology) , inequality , pure mathematics , argument (complex analysis) , convex function , regular polygon , mathematical analysis , geometry , ecology , biochemistry , chemistry , financial economics , economics , biology

We prove some new multidimensional Hardy-type inequalities involving general Hardy type operators with positive kernels for functions Φ which may not necessarily be convex but satisfy the condition Aψ(x) ≤ Φ(x) ≤ Bψ (x), where ψ is convex. Our approach is mainly the use of convexity argument and the results obtained are new even for the one-dimensional case and also unify and extend several inequalities of Hardy type known in the literature.

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