Meda Inequality for Rearrangements of the Convolution on the Heisenberg Group and Some Applications. (16th March 2009)

• Record Type: Journal Article
• Authors: Guliyev, V. S.; Serbetci, A.; Güner, E.; Balcı, S.
• Other Names: Cho Yeol Je Academic Editor.
• Is Part Of: Journal of inequalities and applications. Volume 2009(2009)
• Publication Date: 2009-03-16
• Subjects: Inequalities (Mathematics) -- Periodicals; 512.97
• DOI: 10.1155/2009/864191
• Languages: English
• ISSNs: 1029-242X

Abstract

Abstract : The Meda inequality for rearrangements of the convolution operator on the Heisenberg groupℍ n is proved. By using the Meda inequality, an O'Neil-type inequality for the convolution is obtained. As applications of these results, some sufficient and necessary conditions for the boundedness of the fractional maximal operatorM Ω, α and fractional integral operatorI Ω, α with rough kernels in the spacesL p ( ℍ n ) are found. Finally, we give some comments on the extension of our results to the case of homogeneous groups.