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The Fefferman–Stein Type Inequalities for Strong Fractional Maximal Operators

  • Hiroki SaitoEmail author
  • Hitoshi Tanaka
Article
  • 39 Downloads

Abstract

We prove the Fefferman–Stein type inequalities for strong fractional maximal operators by additional compositions of certain maximal operators instead of using the strong Muckenhoupt weight. With an arbitrary weight, in \({{\mathbb {R}}}^2\), we establish an endpoint estimate and in \({{\mathbb {R}}}^n\), \(n\ge 2\), we give a weak (pp) type estimate for \(p>1\). We also investigate the case \(p=1\) in higher dimensions.

Keywords

Fefferman–Stein type inequality strong maximal operator strong fractional maximal operator 

Mathematics Subject Classification

Primary 42B25 Secondary 42B35 

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.College of Science and TechnologyNihon UniversityFunabashiJapan
  2. 2.Research and Support Center on Higher Education for the Hearing and Visually ImpairedNational University Corporation Tsukuba University of TechnologyTsukubaJapan

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