Kyungpook Mathematical Journal

  • 제46권1호
  • /
  • Pages.31-48
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  • 2006
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  • 1225-6951(pISSN)
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  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
권호 표지

Weighted Lp Boundedness for the Function of Marcinkiewicz

  • Al-Qassem, Hussain M. (Department of Mathematics, Yarmouk University)
  • 투고 : 2004.07.05
  • 발행 : 2006.03.23
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초록

In this paper, we prove a weighted norm inequality for the Marcinkiewicz integral operator $\mathcal{M}_{{\Omega},h}$ when $h$ satisfies a mild regularity condition and ${\Omega}$ belongs to $L(log L)^{1l2}(S^{n-1})$, $n{\geq}2$. We also prove the weighted $L^p$ boundedness for a class of Marcinkiewicz integral operators $\mathcal{M}^*_{{\Omega},h,{\lambda}}$ and $\mathcal{M}_{{\Omega},h,S}$ related to the Littlewood-Paley $g^*_{\lambda}$-function and the area integral S, respectively.

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참고문헌

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