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Weighted Boundedness for the Function of Marcinkiewicz

Hussain M. Al-Qassem
경북대학교 자연과학대학 수학과|2006.03|Kyungpook Mathematical Journal|제46권 제1호|pp. 31-48

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Abstract

In this paper, we prove a weighted norm inequality for the Marcinkiewiczintegral operatorM Ω;h when h satises a mild regularity condition and Ω belongs toL(logL)1l2(Sn 1); n 2. We also prove the weighted Lp boundedness for a class ofMarcinkiewicz integral operatorsMΩ;h; and M Ω;h;S related to the Littlewod-Paleyg-function and the area integralS, respectively.

참고문헌 (14)

  1. "Lp bounds for the function ofMarcinkiewicz", 9, pp.697~700 (2002)
  2. "Weighted boundedness for a class of Marcinkiewiczintegral", 48, pp.1037~1055 (1999), Indiana Univ.
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  4. "Weighted norm inequalities for homogeneous singular integrals", 336, pp.869~880 (1993)
  5. "Singular integral operators with rough kernels supported by sub-varieties", 119, pp.799~839 (1997)
  6. "A weighted norm inequality for rough singular integrals", 51, pp.141~161 (1999)
  7. "Weighted norm inequalities and relatedtopics" (1985)
  8. "Littlewood-Paley and multiplier theorems on weightedLp spaces", 259, pp.235~254 (1980)
  9. "Weighted Lp boundedness of Marcinkiewicz inte-gral", 49(2), pp.211~220 (2004)
  10. "Remarks on square functions in the Littlewood-Paley theory", 58, pp.199~211 (1998)
  11. "Singular integrals and dierentiability properties of functions" (1970), PrincetonUniversity Press Princeton
  12. "Interpolation of operators with change of measures", 87, pp.159~172 (1958)
  13. "A note on the Marcinkiewicz integral", 61-62, pp.235~243 (1990)
  14. "On the function of Marcinkiewicz", pp.203~217 (1972)

관련 논문AI추천

Weighted continuity of multilinear Marcinkiewicz operators for the extreme cases of $p$Liu Lanzhe대한수학회 · 대한수학회논문집2004 · 제19권 제3호Weighted estimates for rough parametric Marcinkiewicz integralsHussain Mohammed Al-Qassem대한수학회 · 대한수학회지2007 · 제44권 제6호Weighted Lp Estimates for a Rough Maximal OperatorH. M. Al-Qassem경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2005 · 제45권 제2호Boundedness of multiple Marcinkiewicz integral operators with rough kernelsHuoxiong Wu대한수학회 · 대한수학회지2006 · 제43권 제3호Weighted inequalities for commutators of potential type operatorsWenming Li대한수학회 · 대한수학회지2007 · 제44권 제6호Sharp Weighted Estimate for Multilinear Singular Integral OperatorLiu Lanzhe대한수학회 · 대한수학회논문집2006 · 제21권 제3호

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