Parabolic Marcinkiewicz integrals on product spaces

Document Type: Research Paper

Author

Department of Mathematics and Statistics‎, ‎Jordan University of Science and Technology‎, ‎Irbid‎, ‎Jordan.

Abstract

‎In this paper‎, ‎we study the $L^p$ ($1<p<\infty$) boundedness for the parabolic Marcinkiewicz integral when the kernel function $\Omega$ belongs to the class $L(\log L)( \mathbf{S}^{n-1}\times\mathbf{S}^{m-1})$‎. ‎Our result essentially extend and improve‎ ‎some known results.

Keywords

Main Subjects


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Volume 42, Issue 6
November and December 2016
Pages 1547-1557
  • Receive Date: 09 January 2014
  • Revise Date: 27 September 2015
  • Accept Date: 29 September 2015