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Multilinear fractional Hausdorff operators

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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 Φ.

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of Wisconsin-Milwaukee, Milwaukee, WI, 53201, USA

    Da Shan Fan

  2. Department of Mathematics, Shanghai University, Shanghai, 200444, P. R. China

    Fa You Zhao

Authors
  1. Da Shan Fan
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  2. Fa You Zhao
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Correspondence to Fa You Zhao.

Additional information

Supported by National Natural Science Foundation of China (Grant Nos. 11201287 and 11201103) and a grant of the First-class Discipline of Universities in Shanghai

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Fan, D.S., Zhao, F.Y. Multilinear fractional Hausdorff operators. Acta. Math. Sin.-English Ser. 30, 1407–1421 (2014). https://doi.org/10.1007/s10114-014-3552-2

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  • DOI: https://doi.org/10.1007/s10114-014-3552-2

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