Multilinear fractional Hausdorff operators

Authors
Fan, Da Shan Zhao, Fa You
Citation
Fan, Da Shan et Zhao, Fa You, Multilinear fractional Hausdorff operators, Acta mathematica Sinica. English series (Print) , 30(8), 2014, pp. 1407-1421
Journal title
Acta mathematica Sinica. English series (Print) → ACNP
ISSN journal
14398516
Volume
30
Issue
8
Year of publication
2014
Pages
1407 - 1421
Database
ACNP
SICI code
Abstract
In this paper, by introducing the space with weak mixed norms, weak type estimates of two kinds of multilinear fractional Hausdorff operators {ie1407-1} and {ie1407-2} on Lebesgue spaces are shown. By virtue of Marcinkiewicz interpolation, strong type estimates of these two operators on Lebesgue spaces are also obtained. Our methods shed some new light on dealing with the case of non-radial function ..