Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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ENDPOINT ESTIMATES FOR MAXIMAL COMMUTATORS IN NON-HOMOGENEOUS SPACES

  • Hu, Guoen (DEPARTMENT OF APPLIED MATHEMATICS UNIVERSITY OF INFORMATION ENGINEERING) ;
  • Meng, Yan (SCHOOL OF INFORMATION RENMIN UNIVERSITY OF CHINA) ;
  • Yang, Dachun (SCHOOL OF MATHEMATICAL SCIENCES BEIJING NORMAL UNIVERSITY)
  • Published : 2007.07.30
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Abstract

Certain weak type endpoint estimates are established for maximal commutators generated by $Calder\acute{o}n-Zygmund$ operators and $Osc_{exp}L^{\gamma}({\mu})$ functions for ${\gamma}{\ge}1$ under the condition that the underlying measure only satisfies some growth condition, where the kernels of $Calder\acute{o}n-Zygmund$ operators only satisfy the standard size condition and some $H\ddot{o}rmander$ type regularity condition, and $Osc_{exp}L^{\gamma}({\mu})$ are the spaces of Orlicz type satisfying that $Osc_{exp}L^{\gamma}({\mu})$ = RBMO(${\mu}$) if ${\gamma}$ = 1 and $Osc_{exp}L^{\gamma}({\mu}){\subset}RBMO({\mu})$ if ${\gamma}$ > 1.

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References

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